Class for a spherical shell and a symmetry with respect to the plane $ z=0 $ . More...

#include <spheric.hpp>

Inheritance diagram for Kadath::Domain_shell:

Public Member Functions
	Domain_shell (int num, int ttype, double r_int, double r_ext, const Point &cr, const Dim_array &nbr)
	Standard constructor : More...

	Domain_shell (const Domain_shell &so)
	Copy constructor. More...

	Domain_shell (int num, FILE *ff)
	Constructor from a file. More...

virtual void	save (FILE *) const
	Saving function. More...

virtual double	get_rmin () const
	Returns the minimum radius. More...

virtual double	get_rmax () const
	Returns the maximum radius. More...

virtual Point	get_center () const
	Returns the center. More...

virtual bool	is_in (const Point &xx, double prec=1e-13) const
	Check whether a point lies inside `Domain`. More...

virtual const Point	absol_to_num (const Point &xxx) const
	Computes the numerical coordinates from the physical ones. More...

virtual const Point	absol_to_num_bound (const Point &, int) const
	Computes the numerical coordinates from the physical ones for a point lying on a boundary. More...

virtual void	do_der_abs_from_der_var (const Val_domain const const der_var, Val_domain **const der_abs) const
	Computes the derivative with respect to the absolute Cartesian coordinates from the derivative with respect to the numerical coordinates. More...

virtual Base_spectral	mult (const Base_spectral &, const Base_spectral &) const
	Method for the multiplication of two `Base_spectral`. More...

virtual Val_domain	mult_cos_phi (const Val_domain &) const
	Multiplication by $\cos \varphi$ . More...

virtual Val_domain	mult_sin_phi (const Val_domain &) const
	Multiplication by $\sin \varphi$ . More...

virtual Val_domain	mult_cos_theta (const Val_domain &) const
	Multiplication by $\cos \theta$ . More...

virtual Val_domain	mult_sin_theta (const Val_domain &) const
	Multiplication by $\sin \theta$ . More...

virtual Val_domain	div_sin_theta (const Val_domain &) const
	Division by $\sin \theta$ . More...

virtual Val_domain	div_cos_theta (const Val_domain &) const
	Division by $\cos \theta$ . More...

virtual Tensor	change_basis_cart_to_spher (int dd, const Tensor &) const
	Changes the tensorial basis from Cartsian to spherical in a given domain. More...

virtual Tensor	change_basis_spher_to_cart (int dd, const Tensor &) const
	Changes the tensorial basis from spherical to Cartesian in a given domain. More...

virtual Val_domain	div_xp1 (const Val_domain &) const
	Division by . More...

virtual Val_domain	div_1mrsL (const Val_domain &) const
	Division by . More...

virtual Val_domain	mult_1mrsL (const Val_domain &) const
	Multiplication by . More...

virtual Val_domain	mult_r (const Val_domain &) const
	Multiplication by . More...

virtual Val_domain	div_r (const Val_domain &) const
	Division by . More...

virtual Val_domain	der_r (const Val_domain &) const
	Compute the radial derivative of a scalar field. More...

virtual Val_domain	der_partial_var (const Val_domain &, int) const
	Partial derivative with respect to a coordinate. More...

virtual Val_domain	ddp (const Val_domain &) const
	Compute the second derivative with respect to $\varphi$ of a scalar field. More...

virtual Val_domain	div_xm1 (const Val_domain &) const
	Division by . More...

virtual Val_domain	mult_xm1 (const Val_domain &) const
	Multiplication by . More...

virtual Val_domain	div_1mx2 (const Val_domain &) const
	Division by . More...

virtual Val_domain	laplacian2 (const Val_domain &, int) const
	Computes the ordinary flat 2dè- Laplacian for a scalar field with an harmonic index `m`. More...

virtual Val_domain	dt (const Val_domain &) const
	Compute the derivative with respect to $\theta$ of a scalar field. More...

virtual double	multipoles_sym (int, int, int, const Val_domain &, const Array< double > &) const
	Extraction of a given multipole, at some boundary, for a symmetric scalar function. More...

virtual double	multipoles_asym (int, int, int, const Val_domain &, const Array< double > &) const
	Extraction of a given multipole, at some boundary, for a anti-symmetric scalar function. More...

virtual Term_eq	multipoles_sym (int, int, int, const Term_eq &, const Array< double > &) const
	Extraction of a given multipole, at some boundary, for a symmetric scalar function. More...

virtual Term_eq	multipoles_asym (int, int, int, const Term_eq &, const Array< double > &) const
	Extraction of a given multipole, at some boundary, for an anti-symmetric scalar function. More...

virtual Term_eq	radial_part_sym (const Space &, int, int, const Term_eq &, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &), const Param &) const
	Gives some radial fit for a given multipole, intended for symmetric scalar function. More...

virtual Term_eq	radial_part_asym (const Space &, int, int, const Term_eq &, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &), const Param &) const
	Gives some radial fit for a given multipole, intended for anti-symmetric scalar function. More...

virtual Term_eq	harmonics_sym (const Term_eq &, const Term_eq &, int, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &), const Param &, const Array< double > &) const
	Fit, spherical harmonic by spherical harmonic, for a symmetric function. More...

virtual Term_eq	harmonics_asym (const Term_eq &, const Term_eq &, int, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &), const Param &, const Array< double > &) const
	Fit, spherical harmonic by spherical harmonic, for an anti-symmetric function. More...

virtual Term_eq	der_radial_part_sym (const Space &, int, int, const Term_eq &, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &param), const Param &) const
	Gives some radial fit for a given multipole, intended for the radial derivative of a symmetric scalar function. More...

virtual Term_eq	der_radial_part_asym (const Space &, int, int, const Term_eq &, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &), const Param &) const
	Gives some radial fit for a given multipole, intended for the radial derivative of an anti-symmetric scalar function. More...

virtual Term_eq	der_harmonics_sym (const Term_eq &, const Term_eq &, int, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &), const Param &, const Array< double > &) const
	Fit, spherical harmonic by spherical harmonic, for the radial derivative of a symmetric function. More...

virtual Term_eq	der_harmonics_asym (const Term_eq &, const Term_eq &, int, Term_eq(*f)(const Space &, int, int, const Term_eq &, const Param &), const Param &, const Array< double > &) const
	Fit, spherical harmonic by spherical harmonic, for the radial derivative of an anti-symmetric function. More...

virtual Term_eq	der_multipoles_sym (int, int, int, const Term_eq &, const Array< double > &) const
	Extraction of a given multipole, at some boundary, for the radial derivative a symmetric scalar function. More...

virtual Term_eq	der_multipoles_asym (int, int, int, const Term_eq &, const Array< double > &) const
	Extraction of a given multipole, at some boundary, for the radial derivative of an anti-symmetric scalar function. More...

Term_eq	bc_waves (const Term_eq &gamma, const Term_eq &omega) const
	Gives an matching of the spatial metric, based on homogeneous solutions of outgoing waves. More...

Tensor	bc_waves (int dom, const Tensor &gamma, const double omega, bool toinf=true) const
	Gives an matching of the spatial metric, based on homogeneous solutions of outgoing waves. More...

Val_domain	fitschwarz (const Val_domain &, int) const
	Fit some field with a decay (`Val_domain` version). More...

Term_eq	fitschwarz (const Term_eq &, int) const
	Fit some field with a decay (`Term_eq` version). More...

virtual void	find_other_dom (int, int, int &, int &) const
	Gives the informations corresponding the a touching neighboring domain. More...

virtual Val_domain	der_normal (const Val_domain &, int) const
	Normal derivative with respect to a given surface. More...

virtual double	val_boundary (int, const Val_domain &, const Index &) const
	Computes the value of a field at a boundary. More...

virtual int	nbr_unknowns (const Tensor &, int) const
	Computes the number of true unknowns of a `Tensor`, in a given domain. More...

int	nbr_unknowns_val_domain_mquant (const Val_domain &so, int mquant) const
	Computes the number of true unknowns of a `Val_domain`. More...

int	nbr_unknowns_val_domain (const Val_domain &so, int mlim) const
	Computes the number of true unknowns of a `Val_domain`. More...

virtual Array< int >	nbr_conditions (const Tensor &, int, int, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Computes number of discretized equations associated with a given tensorial equation in the bulk. More...

int	nbr_conditions_val_domain_mquant (const Val_domain &so, int mquant, int order) const
	Computes number of discretized equations associated with a given tensorial equation in the bulk. More...

int	nbr_conditions_val_domain (const Val_domain &so, int mlim, int order) const
	Computes number of discretized equations associated with a given tensorial equation in the bulk. More...

virtual Array< int >	nbr_conditions_boundary (const Tensor &, int, int, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Computes number of discretized equations associated with a given tensorial equation on a boundary. More...

int	nbr_conditions_val_domain_boundary_mquant (const Val_domain &so, int mquant) const
	Computes number of discretized equations associated with a given equation on a boundary. More...

int	nbr_conditions_val_domain_boundary (const Val_domain &so, int mlim) const
	Computes number of discretized equations associated with a given equation on a boundary. More...

virtual void	export_tau (const Tensor &, int, int, Array< double > &, int &, const Array< int > &, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Exports all the residual equations corresponding to a tensorial one in the bulk. More...

void	export_tau_val_domain_mquant (const Val_domain &eq, int mquant, int order, Array< double > &res, int &pos_res, int ncond) const
	Exports a residual equation in the bulk. More...

void	export_tau_val_domain (const Val_domain &eq, int mlim, int order, Array< double > &res, int &pos_res, int ncond) const
	Exports a residual equation in the bulk. More...

virtual void	export_tau_boundary (const Tensor &, int, int, Array< double > &, int &, const Array< int > &, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Exports all the residual equations corresponding to a tensorial one on a given boundary It makes use of the various Galerkin basis used. More...

void	export_tau_val_domain_boundary_mquant (const Val_domain &eq, int mquant, int bound, Array< double > &res, int &pos_res, int ncond) const
	Exports all the residual equations corresponding to a tensorial one on a given boundary It makes use of the various Galerkin basis used. More...

void	export_tau_val_domain_boundary (const Val_domain &eq, int mlim, int bound, Array< double > &res, int &pos_res, int ncond) const
	Exports all the residual equations corresponding to a tensorial one on a given boundary It makes use of the various Galerkin basis used. More...

virtual void	affecte_tau (Tensor &, int, const Array< double > &, int &) const
	Affects some coefficients to a `Tensor`. More...

void	affecte_tau_val_domain_mquant (Val_domain &so, int mquant, const Array< double > &cf, int &pos_cf) const
	Affects some coefficients to a `Val_domain`. More...

void	affecte_tau_val_domain (Val_domain &so, int mlim, const Array< double > &cf, int &pos_cf) const
	Affects some coefficients to a `Val_domain`. More...

virtual void	affecte_tau_one_coef (Tensor &, int, int, int &) const
	Sets at most one coefficient of a `Tensor` to 1. More...

void	affecte_tau_one_coef_val_domain_mquant (Val_domain &so, int mquant, int cc, int &pos_cf) const
	Sets at most one coefficient of a `Val_domain` to 1. More...

void	affecte_tau_one_coef_val_domain (Val_domain &so, int mlim, int cc, int &pos_cf) const
	Sets at most one coefficient of a `Val_domain` to 1. More...

virtual void	export_tau_boundary_exception (const Tensor &, int, int, Array< double > &, int &, const Array< int > &, const Param &, int, const Tensor &, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Exports all the residual equations corresponding to one tensorial one on a given boundary, excepted for some coefficients where another equation is used. More...

void	export_tau_val_domain_boundary_exception_mquant (const Val_domain &eq, int mquant, int bound, Array< double > &res, int &pos_res, int ncond, const Param &param, int type_exception, const Val_domain &exception) const
	Exports all the residual equations corresponding to one tensorial one on a given boundary, excepted for some coefficients where another equation is used. More...

void	export_tau_val_domain_boundary_exception (const Val_domain &eq, int mlim, int bound, Array< double > &res, int &pos_res, int ncond, const Param &param, int type_exception, const Val_domain &exception) const
	Exports all the residual equations corresponding to one tensorial one on a given boundary, excepted for some coefficients where another equation is used. More...

virtual int	nbr_points_boundary (int, const Base_spectral &) const
	Computes the number of relevant collocation points on a boundary. More...

virtual void	do_which_points_boundary (int, const Base_spectral &, Index **, int) const
	Lists all the indices corresponding to true collocation points on a boundary. More...

virtual Tensor	import (int, int, int, const Array< int > &, Tensor **) const
	Gets the value of a `Tensor` by importing data from neighboring domains, on a boundary. More...

virtual double	integ_volume (const Val_domain &so) const
	Volume integral. More...

virtual Term_eq	derive_flat_spher (int, char, const Term_eq &, const Metric *) const
	Computes the flat derivative of a `Term_eq`, in spherical orthonormal coordinates. More...

virtual Term_eq	derive_flat_cart (int, char, const Term_eq &, const Metric *) const
	Computes the flat derivative of a `Term_eq`, in Cartesian coordinates. More...

virtual Term_eq	derive_flat_mtz (int, char, const Term_eq &, const Metric *) const
	Computes the flat derivative of a `Term_eq`, in spherical coordinates where the constant radii sections have a negative curvature. More...

virtual double	integ (const Val_domain &so, int bound) const
	Surface integral on a given boundary. More...

virtual ostream &	print (ostream &o) const
	Delegate function to virtualize the << operator. More...

int	get_num () const
	Returns the index of the curent domain. More...

Dim_array const &	get_nbr_points () const
	Returns the number of points. More...

Dim_array const &	get_nbr_coefs () const
	Returns the number of coefficients. More...

int	get_ndim () const
	Returns the number of dimensions. More...

int	get_type_base () const
	Returns the type of the basis. More...

Array< double > const &	get_coloc (int) const
	Returns the colocation points for a given variable. More...

virtual const Val_domain &	get_chi () const
	Returns the variable $\chi$ . More...

virtual const Val_domain &	get_eta () const
	Returns the variable $\eta$ . More...

virtual const Val_domain &	get_X () const
	Returns the variable . More...

virtual const Val_domain &	get_T () const
	Returns the variable . More...

Val_domain const &	get_absol (int i) const
	Returns the absolute coordinates. More...

Val_domain const &	get_radius () const
	Returns the generalized radius. More...

Val_domain const &	get_cart (int i) const
	Returns a Cartesian coordinates. More...

Val_domain const &	get_cart_surr (int i) const
	Returns a Cartesian coordinates divided by the radius. More...

virtual Val_domain	div_x (const Val_domain &) const
	Division by . More...

virtual Val_domain	div_chi (const Val_domain &) const
	Division by $\chi$ . More...

virtual Val_domain	div_sin_chi (const Val_domain &) const
	Division by $\sin \chi$ . More...

virtual Val_domain	mult_cos_time (const Val_domain &) const
	Multiplication by $\cos \omega t$ . More...

virtual Val_domain	mult_sin_time (const Val_domain &) const
	Multiplication by $\sin \omega t$ . More...

virtual Val_domain	laplacian (const Val_domain &so, int m) const
	Computes the ordinary flat Laplacian for a scalar field with an harmonic index `m`. More...

virtual Val_domain	der_t (const Val_domain &so) const
	Compute the derivative with respect to $\theta$ of a scalar field. More...

virtual Val_domain	der_p (const Val_domain &so) const
	Compute the derivative with respect to $\varphi$ of a scalar field. More...

virtual Val_domain	der_r_rtwo (const Val_domain &so) const
	Compute the radial derivative multiplied by of a scalar field. More...

virtual Val_domain	srdr (const Val_domain &so) const
	Compute the of a scalar field . More...

virtual Val_domain	ddr (const Val_domain &so) const
	Compute the second radial derivative w of a scalar field. More...

virtual Val_domain	ddt (const Val_domain &so) const
	Compute the second derivative with respect to $\theta$ of a scalar field. More...

virtual Val_domain	dtime (const Val_domain &so) const
	Computes the time derivative of a field. More...

virtual Val_domain	ddtime (const Val_domain &so) const
	Computes the second time derivative of a field. More...

virtual const Term_eq *	give_normal (int bound, int tipe) const
	Returns the vector normal to a surface. More...

virtual Term_eq	der_normal_term_eq (const Term_eq &so, int bound) const
	Returns the normal derivative of a `Term_eq`. More...

virtual Term_eq	div_1mx2_term_eq (const Term_eq &) const
	Returns the division by of a `Term_eq`. More...

virtual Term_eq	lap_term_eq (const Term_eq &so, int m) const
	Returns the flat Laplacian of `Term_eq`, for a given harmonic. More...

virtual Term_eq	lap2_term_eq (const Term_eq &so, int m) const
	Returns the flat 2d-Laplacian of `Term_eq`, for a given harmonic. More...

virtual Term_eq	mult_r_term_eq (const Term_eq &so) const
	Multiplication by of a `Term_eq`. More...

virtual Term_eq	integ_volume_term_eq (const Term_eq &so) const
	Volume integral of a `Term_eq`. More...

virtual Term_eq	grad_term_eq (const Term_eq &so) const
	Gradient of `Term_eq`. More...

virtual Term_eq	div_r_term_eq (const Term_eq &) const
	Division by of a `Term_eq`. More...

virtual Term_eq	integ_term_eq (const Term_eq &so, int bound) const
	Surface integral of a `Term_eq`. More...

virtual Term_eq	dr_term_eq (const Term_eq &so) const
	Radial derivative of a `Term_eq`. More...

virtual Term_eq	dtime_term_eq (const Term_eq &so) const
	Time derivative of a `Term_eq`. More...

virtual Term_eq	ddtime_term_eq (const Term_eq &so) const
	Second time derivative of a `Term_eq`. More...

virtual int	nbr_unknowns_from_adapted () const
	Gives the number of unknowns coming from the variable shape of the domain. More...

virtual void	vars_to_terms () const
	The `Term_eq` describing the variable shape of the `Domain` are updated. More...

virtual void	affecte_coef (int &conte, int cc, bool &found) const
	The variation of the functions describing the shape of the `Domain` are affected from the unknowns of the system. More...

virtual void	xx_to_vars_from_adapted (Val_domain &shape, const Array< double > &xx, int &conte) const
	Computes the new boundary of a `Domain` from a set of values. More...

virtual void	xx_to_vars_from_adapted (double bound, const Array< double > &xx, int &conte) const
	Computes the new boundary of a `Domain` from a set of values. More...

virtual void	xx_to_ders_from_adapted (const Array< double > &xx, int &conte) const
	Affects the derivative part of variable a `Domain` from a set of values. More...

virtual void	update_term_eq (Term_eq *so) const
	Update the value of a field, after the shape of the `Domain` has been changed by the system. More...

virtual void	update_variable (const Val_domain &shape, const Scalar &oldval, Scalar &newval) const
	Update the value of a scalar, after the shape of the `Domain` has been changed by the system. More...

virtual void	update_variable (double bound, const Scalar &oldval, Scalar &newval) const
	Update the value of a scalar, after the shape of the `Domain` has been changed by the system. More...

virtual void	update_constante (const Val_domain &shape, const Scalar &oldval, Scalar &newval) const
	Update the value of a scalar, after the shape of the `Domain` has been changed by the system. More...

virtual void	update_constante (double bound, const Scalar &oldval, Scalar &newval) const
	Update the value of a scalar, after the shape of the `Domain` has been changed by the system. More...

virtual void	update_mapping (const Val_domain &shape)
	Updates the variables parts of the `Domain`. More...

virtual void	update_mapping (double bound)
	Updates the variables parts of the `Domain`. More...

virtual void	set_val_inf (Val_domain &so, double xx) const
	Sets the value at infinity of a `Val_domain` : not implemented for this type of `Domain`. More...

virtual Val_domain	mult_x (const Val_domain &so) const
	Multiplication by . More...

virtual double	integrale (const Val_domain &so) const
	Volume integral. More...

virtual Term_eq	partial_spher (const Term_eq &so) const
	Computes the part of the gradient containing the partial derivative of the field, in spherical orthonormal coordinates. More...

virtual Term_eq	partial_cart (const Term_eq &so) const
	Computes the part of the gradient containing the partial derivative of the field, in Cartesian coordinates. More...

virtual Term_eq	partial_mtz (const Term_eq &so) const
	Computes the part of the gradient containing the partial derivative of the field, in orthonormal coordinates where the constant radius sections have negative curvature. More...

virtual Term_eq	connection_spher (const Term_eq &so) const
	Computes the part of the gradient involving the connections, in spherical orthonormal coordinates. More...

virtual Term_eq	connection_mtz (const Term_eq &so) const
	Computes the part of the gradient involving the connections, in spherical coordinates where the constant radius sections have negative curvature. More...

virtual Array< int >	nbr_conditions_array (const Tensor &eq, int dom, const Array< int > &order, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Computes number of discretized equations associated with a given tensorial equation in the bulk. More...

virtual Array< int >	nbr_conditions_boundary_array (const Tensor &eq, int dom, int bound, const Array< int > &order, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Computes number of discretized equations associated with a given tensorial equation on a boundary. More...

virtual void	export_tau_array (const Tensor &eq, int dom, const Array< int > &order, Array< double > &res, int &pos_res, const Array< int > &ncond, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Exports all the residual equations corresponding to one tensorial one in the bulk. More...

virtual void	export_tau_boundary_array (const Tensor &eq, int dom, int bound, const Array< int > &order, Array< double > &res, int &pos_res, const Array< int > &ncond, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Exports all the residual equations corresponding to one tensorial one on a given boundary It makes use of the various Galerkin basis used. More...

virtual Array< int >	nbr_conditions_boundary_one_side (const Tensor &eq, int dom, int bound, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Computes number of discretized equations associated with a given tensorial equation on a boundary. More...

virtual void	export_tau_boundary_one_side (const Tensor &eq, int dom, int bound, Array< double > &res, int &pos_res, const Array< int > &ncond, int n_cmp=-1, Array< int > **p_cmp=0x0) const
	Exports all the residual equations corresponding to one tensorial one on a given boundary. More...

Term_eq	import (int numdom, int bound, int n_ope, Term_eq **parts) const
	Gets the value of a `Term_eq` by importing data from neighboring domains, on a boundary. More...

virtual void	filter (Tensor &tt, int dom, double treshold) const
	Puts to zero all the coefficients below a given treshold. More...

Protected Member Functions
virtual void	del_deriv ()
	Destroys the derivated members (like `coloc`, `cart` and `radius`), when changing the type of colocation points. More...

Term_eq	do_comp_by_comp (const Term_eq &so, Val_domain(Domain::*pfunc)(const Val_domain &) const) const
	Function used to apply the same operation to all the components of a tensor, in the current domain. More...

Term_eq	do_comp_by_comp_with_int (const Term_eq &so, int val, Val_domain(Domain::*pfunc)(const Val_domain &, int) const) const
	Function used to apply the same operation to all the components of a tensor, in the current domain. More...

Protected Attributes
int	num_dom
	Number of the current domain (used by the `Space`) More...

int	ndim
	Number of dimensions. More...

Dim_array	nbr_points
	Number of colocation points. More...

Dim_array	nbr_coefs
	Number of coefficients. More...

int	type_base
	Type of colocation point : More...

Memory_mapped_array< Array< double > * >	coloc
	Colocation points in each dimension (stored in `ndim` 1d- arrays) More...

Memory_mapped_array< Val_domain * >	absol
	Asbolute coordinates (if defined ; usually Cartesian-like) More...

Memory_mapped_array< Val_domain * >	cart
	Cartesian coordinates. More...

Val_domain *	radius
	The generalized radius. More...

Memory_mapped_array< Val_domain * >	cart_surr
	Cartesian coordinates divided by the radius. More...

Private Member Functions
virtual void	do_absol () const
	Computes the absolute coordinates. More...

virtual void	do_radius () const
	Computes the generalized radius. More...

virtual void	do_cart () const
	Computes the Cartesian coordinates. More...

virtual void	do_cart_surr () const
	Computes the Cartesian coordinates over the radius. More...

virtual void	set_cheb_base (Base_spectral &so) const
	Sets the base to the standard one for Chebyshev polynomials. More...

virtual void	set_cheb_base_with_m (Base_spectral &so, int m) const
	Gives the standard base using Chebyshev polynomials. More...

virtual void	set_legendre_base (Base_spectral &so) const
	Sets the base to the standard one for Legendre polynomials. More...

virtual void	set_anti_cheb_base (Base_spectral &so) const
	Sets the base to the standard one for Chebyshev polynomials for functions antisymetric in The bases are : More...

virtual void	set_anti_legendre_base (Base_spectral &so) const
	Sets the base to the standard one for Legendre polynomials for functions antisymetric in The bases are : More...

virtual void	set_cheb_base_r_spher (Base_spectral &) const
	Gives the base using Chebyshev polynomials, for the radial component of a vector. More...

virtual void	set_cheb_base_t_spher (Base_spectral &) const
	Gives the base using Chebyshev polynomials, for the $\theta$ component of a vector. More...

virtual void	set_cheb_base_p_spher (Base_spectral &) const
	Gives the base using Chebyshev polynomials, for the $\varphi$ component of a vector. More...

virtual void	set_cheb_base_r_mtz (Base_spectral &) const
	Gives the base using Chebyshev polynomials, for the radial component of a vector in the MTZ setting. More...

virtual void	set_cheb_base_t_mtz (Base_spectral &) const
	Gives the base using Chebyshev polynomials, for the $\theta$ component of a vector in the MTZ setting. More...

virtual void	set_cheb_base_p_mtz (Base_spectral &) const
	Gives the base using Chebyshev polynomials, for the $\varphi$ component of a vector in the MTZ setting. More...

virtual void	set_legendre_base_r_spher (Base_spectral &) const
	Gives the base using Legendre polynomials, for the radial component of a vector. More...

virtual void	set_legendre_base_t_spher (Base_spectral &) const
	Gives the base using Legendre polynomials, for the $\theta$ component of a vector. More...

virtual void	set_legendre_base_p_spher (Base_spectral &) const
	Gives the base using Legendre polynomials, for the $\varphi$ component of a vector. More...

virtual void	set_legendre_base_r_mtz (Base_spectral &) const
	Gives the base using Legendre polynomials, for the radial component of a vector in the MTZ context. More...

virtual void	set_legendre_base_t_mtz (Base_spectral &) const
	Gives the base using Legendre polynomials, for the $\theta$ component of a vector in the MTZ context. More...

virtual void	set_legendre_base_p_mtz (Base_spectral &) const
	Gives the base using Legendre polynomials, for the $\varphi$ component of a vector in the MTZ context. More...

virtual void	set_cheb_r_base (Base_spectral &) const
	Gives the base using odd Chebyshev polynomials$ for the radius. More...

virtual void	set_legendre_r_base (Base_spectral &) const
	Gives the base using odd Legendre polynomials$ for the radius. More...

virtual void	do_coloc ()
	Computes the colocation points. More...

virtual int	give_place_var (char *) const
	Translates a name of a coordinate into its corresponding numerical name. More...

virtual void	set_legendre_base_with_m (Base_spectral &so, int m) const
	Gives the stnadard base using Legendre polynomials. More...

virtual void	set_anti_cheb_base_with_m (Base_spectral &so, int m) const
	Gives the base using Chebyshev polynomials, for functions antisymetric with respect to . More...

virtual void	set_anti_legendre_base_with_m (Base_spectral &so, int m) const
	Gives the base using Legendre polynomials, for functions antisymetric with respect to . More...

virtual void	set_cheb_base_rt_spher (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the $(r, \theta)$ component of a 2-tensor. More...

virtual void	set_cheb_base_rp_spher (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the $(r, \varphi)$ component of a 2-tensor. More...

virtual void	set_cheb_base_tp_spher (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the $(\theta, \varphi)$ component of a 2-tensor. More...

virtual void	set_cheb_base_x_cart (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the component of a vector. More...

virtual void	set_cheb_base_y_cart (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the component of a vector. More...

virtual void	set_cheb_base_z_cart (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the component of a vector. More...

virtual void	set_cheb_base_xy_cart (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the component of a vector. More...

virtual void	set_cheb_base_xz_cart (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the component of a vector. More...

virtual void	set_cheb_base_yz_cart (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for the component of a vector. More...

virtual void	set_legendre_base_x_cart (Base_spectral &so) const
	Gives the base using Legendre polynomials, for the component of a vector. More...

virtual void	set_legendre_base_y_cart (Base_spectral &so) const
	Gives the base using Legendre polynomials, for the component of a vector. More...

virtual void	set_legendre_base_z_cart (Base_spectral &so) const
	Gives the base using Legendre polynomials, for the component of a vector. More...

virtual void	set_cheb_xodd_base (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for odd functions in (critic space case) More...

virtual void	set_legendre_xodd_base (Base_spectral &so) const
	Gives the base using Legendre polynomials, for odd functions in (critic space case) More...

virtual void	set_cheb_todd_base (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for odd functions in (critic space case) More...

virtual void	set_legendre_todd_base (Base_spectral &so) const
	Gives the base using Legendre polynomials, for odd functions in (critic space case) More...

virtual void	set_cheb_xodd_todd_base (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for odd functions in and in (critic space case) More...

virtual void	set_legendre_xodd_todd_base (Base_spectral &so) const
	Gives the base using Chebyshev polynomials, for odd functions in and in (critic space case) More...

virtual void	set_cheb_base_odd (Base_spectral &so) const
	Gives the base using odd Chebyshev polynomials$. More...

virtual void	set_legendre_base_odd (Base_spectral &so) const
	Gives the base using odd Legendre polynomials$. More...

Private Attributes
double	alpha
	Relates the numerical to the physical radii. More...

double	beta
	Relates the numerical to the physical radii. More...

Point	center
	Absolute coordinates of the center. More...

Friends
class	Domain_shell_log

class	Domain_shell_surr

Detailed Description

Class for a spherical shell and a symmetry with respect to the plane $ z=0 $ .

3 dimensions.
centered on the point center
The numerical coordinates are :

$-1 \leq x \leq 1$

$0 \leq \theta^\star \leq \pi/2$

$0 \leq \varphi^\star < 2\pi$

Standard spherical coordinates :

$r = \alpha x + \beta$

$\theta = \theta^\star$

$\varphi = \varphi^\star$

Standard Cartesian coordinates :

$X = r \sin\theta \cos\varphi + Xc$

$Y = r \sin\theta \sin\varphi + Yc$

$Z = r \cos\theta + Zc$

Definition at line 555 of file spheric.hpp.

Constructor & Destructor Documentation

◆ Domain_shell() [1/3]

Kadath::Domain_shell::Domain_shell	(	int	num,
		int	ttype,
		double	r_int,
		double	r_ext,
		const Point &	cr,
		const Dim_array &	nbr
	)

Standard constructor :

Parameters

num	: number of the domain (used by the `Space`).
ttype	: Chebyshev or Legendre type of spectral expansion.
r_int	: inner radius of the shell.
r_ext	: outer radius of the shell.
cr	: center of the spherical coordinates.
nbr	: number of points in each dimension.

Definition at line 28 of file domain_shell.cpp.

References do_coloc(), Kadath::Dim_array::get_ndim(), and Kadath::Point::get_ndim().

◆ Domain_shell() [2/3]

Kadath::Domain_shell::Domain_shell ( const Domain_shell & so )

Copy constructor.

Definition at line 39 of file domain_shell.cpp.

◆ Domain_shell() [3/3]

Kadath::Domain_shell::Domain_shell	(	int	num,
		FILE *	ff
	)

Constructor from a file.

Parameters

num	: number of the domain (used by the `Space`).
ff	file containd the domain, generated by the save function.

Definition at line 44 of file domain_shell.cpp.

References alpha, beta, and do_coloc().

Member Function Documentation

◆ absol_to_num()

const Point Kadath::Domain_shell::absol_to_num ( const Point & xxx ) const

virtual

Computes the numerical coordinates from the physical ones.

$x = \displaystyle\frac{\sqrt{(X-X_c)^2+(Y-Y_c)^2+(Z-Z_c)^2}-\beta}{\alpha}$
$\theta^\star = {\rm atan} (\displaystyle\frac{\sqrt{(X-X_c)^2+(Y-Y_c)^2}}{Z-Z_c})$
$\varphi^\star = {\rm atan} (\displaystyle\frac{Y-Y_c}{Z-Z_c})$
Parameters

xxx [input] : the absolute Cartesian coordinates of the point.

Returns
the numerical coordinates $(x, \theta^\star, \varphi^\star)$ .

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 183 of file domain_shell.cpp.

References alpha, beta, center, is_in(), and Kadath::Point::set().

◆ absol_to_num_bound()

const Point Kadath::Domain_shell::absol_to_num_bound	(	const Point &	xxx,
		int	bound
	)		const

virtual

Computes the numerical coordinates from the physical ones for a point lying on a boundary.

Parameters

xxx	[input] : the absolute Cartesian coordinates of the point.
bound	[input] : the boundary.

Returns: the numerical coordinates.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 212 of file domain_shell.cpp.

References center, is_in(), and Kadath::Point::set().

◆ affecte_coef()

virtual void Kadath::Domain::affecte_coef	(	int &	conte,
		int	cc,
		bool &	found
	)		const

inlinevirtualinherited

The variation of the functions describing the shape of the Domain are affected from the unknowns of the system.

Parameters

conte	: current position if the unknowns.
cc	: position of the unknown to be set.
found	: `true` if the index was indeed corresponding to one of the coefficients of the variable domain.

Reimplemented in Kadath::Domain_shell_outer_homothetic, Kadath::Domain_shell_inner_homothetic, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 906 of file space.hpp.

◆ affecte_tau()

void Kadath::Domain_shell::affecte_tau	(	Tensor &	so,
		int	dom,
		const Array< double > &	cf,
		int &	pos_cf
	)		const

virtual

Affects some coefficients to a Tensor.

It takes into account the various symmetries and regularity conditions (by means of Garlekin basis).

Parameters

so	: the `Tensor` to be affected.
dom	: the domain considered (should be the same as num_dom).
cf	: `Array` of the coefficients used.
pos_cf	: current position in the array of coefficients.

Reimplemented from Kadath::Domain.

Definition at line 224 of file domain_shell_affecte_tau.cpp.

References affecte_tau_val_domain(), affecte_tau_val_domain_mquant(), Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Space::get_domain(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_m_quant_affected(), Kadath::Tensor::set(), and Kadath::Scalar::set_domain().

◆ affecte_tau_one_coef()

void Kadath::Domain_shell::affecte_tau_one_coef	(	Tensor &	so,
		int	dom,
		int	cc,
		int &	pos_cf
	)		const

virtual

Sets at most one coefficient of a Tensor to 1.

It takes into account the various symmetries and regularity conditions (by means of Garlekin basis).

Parameters

so	: the `Tensor` to be affected. It is set to zero if cc does not corresponds to another field.
dom	: the domain considered (should be the same as num_dom).
cc	: location, in the overall system, of the coefficient to be set to 1.
pos_cf	: current position.

Reimplemented from Kadath::Domain.

Definition at line 179 of file domain_shell_affecte_tau_one_coef.cpp.

References affecte_tau_one_coef_val_domain(), affecte_tau_one_coef_val_domain_mquant(), Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Space::get_domain(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_m_quant_affected(), Kadath::Tensor::set(), and Kadath::Scalar::set_domain().

◆ affecte_tau_one_coef_val_domain()

void Kadath::Domain_shell::affecte_tau_one_coef_val_domain	(	Val_domain &	so,
		int	mlim,
		int	cc,
		int &	pos_cf
	)		const

Sets at most one coefficient of a Val_domain to 1.

It takes into account the various symmetries and regularity conditions (by means of Garlekin basis).

Parameters

so	: the `Val_domain` to be affected. It is set to zero if cc does not corresponds to another field.
mlim	: limit for the regularity.
cc	: location, in the overall system, of the coefficient to be set to 1.
pos_cf	: current position.

Definition at line 98 of file domain_shell_affecte_tau_one_coef.cpp.

References Kadath::Val_domain::allocate_coef(), Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::get_base(), Kadath::Val_domain::is_zero, Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), Kadath::Index::set(), and Kadath::Val_domain::set_zero().

◆ affecte_tau_one_coef_val_domain_mquant()

void Kadath::Domain_shell::affecte_tau_one_coef_val_domain_mquant	(	Val_domain &	so,
		int	mquant,
		int	cc,
		int &	pos_cf
	)		const

Sets at most one coefficient of a Val_domain to 1.

It takes into account the various symmetries and regularity conditions (by means of Garlekin basis).

Parameters

so	: the `Val_domain` to be affected. It is set to zero if cc does not corresponds to another field.
mquant	: limit for the regularity .
cc	: location, in the overall system, of the coefficient to be set to 1.
pos_cf	: current position.

Definition at line 28 of file domain_shell_affecte_tau_one_coef.cpp.

References Kadath::Val_domain::allocate_coef(), Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::get_base(), Kadath::Val_domain::is_zero, Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), Kadath::Index::set(), and Kadath::Val_domain::set_zero().

◆ affecte_tau_val_domain()

void Kadath::Domain_shell::affecte_tau_val_domain	(	Val_domain &	so,
		int	mlim,
		const Array< double > &	cf,
		int &	pos_cf
	)		const

Affects some coefficients to a Val_domain.

It takes into account the various symmetries and regularity conditions (by means of Garlekin basis).

Parameters

so	: the field to be affected.
mlim	: limit for the regularity.
cf	: `Array` of the coefficients used.
pos_cf	: current position in the array of coefficients.

Definition at line 117 of file domain_shell_affecte_tau.cpp.

References Kadath::Val_domain::allocate_coef(), Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::get_base(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), and Kadath::Index::set().

◆ affecte_tau_val_domain_mquant()

void Kadath::Domain_shell::affecte_tau_val_domain_mquant	(	Val_domain &	so,
		int	mquant,
		const Array< double > &	cf,
		int &	pos_cf
	)		const

Affects some coefficients to a Val_domain.

It takes into account the various symmetries and regularity conditions (by means of Garlekin basis).

Parameters

so	: the field to be affected.
mquant	: quantum number wrt $\varphi$ .
cf	: `Array` of the coefficients used.
pos_cf	: current position in the array of coefficients.

Definition at line 28 of file domain_shell_affecte_tau.cpp.

References Kadath::Val_domain::allocate_coef(), Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::get_base(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), and Kadath::Index::set().

◆ bc_waves() [1/2]

Term_eq Kadath::Domain_shell::bc_waves	(	const Term_eq &	gamma,
		const Term_eq &	omega
	)		const

Gives an matching of the spatial metric, based on homogeneous solutions of outgoing waves.

Parameters

gamma	: the metric.
omega	: the angular velocity of the helical Killing vector.

Returns: : the outgoing wave.

Definition at line 33 of file bc_waves.cpp.

References Kadath::Val_domain::allocate_coef(), Kadath::Term_eq::der_d, Kadath::Term_eq::der_t, Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_n_comp(), Kadath::Domain::get_radius(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::indices(), multipoles_asym(), multipoles_sym(), Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Tensor::set(), Kadath::Index::set(), Kadath::Val_domain::set_coef(), Kadath::Scalar::set_domain(), Kadath::Tensor::std_base(), Kadath::Term_eq::type_data, Kadath::Term_eq::val_d, and Kadath::Term_eq::val_t.

◆ bc_waves() [2/2]

Tensor Kadath::Domain_shell::bc_waves	(	int	dom,
		const Tensor &	gamma,
		const double	omega,
		bool	toinf = `true`
	)		const

Gives an matching of the spatial metric, based on homogeneous solutions of outgoing waves.

Tensor version

Parameters

dom	: the domain (should be the same as num_dom)
gamma	: the metric.
omega	: the angular velocity of the helical Killing vector.
toinf	: has to do where the matching is performed... (need to clarify that)

Returns: : the outgoing wave.

Definition at line 34 of file bc_waves_tensor.cpp.

References Kadath::Val_domain::allocate_coef(), Kadath::Val_domain::coef(), der_r(), Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Val_domain::get_coef(), Kadath::Tensor::get_n_comp(), Kadath::Domain::get_radius(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::indices(), multipoles_asym(), multipoles_sym(), Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Tensor::set(), Kadath::Index::set(), Kadath::Val_domain::set_coef(), Kadath::Scalar::set_domain(), Kadath::Tensor::std_base(), and Kadath::Val_domain::std_base().

◆ change_basis_cart_to_spher()

Tensor Kadath::Domain_shell::change_basis_cart_to_spher	(	int	dd,
		const Tensor &	so
	)		const

virtual

Changes the tensorial basis from Cartsian to spherical in a given domain.

Parameters

dd	[input] : the domain. Should be consistent with *this.
so	[input] : the input tensor.

Returns: the tensor in spherical tensorial basis in the current domain.

Reimplemented from Kadath::Domain.

Definition at line 94 of file domain_shell_change_basis_tensor.cpp.

◆ change_basis_spher_to_cart()

Tensor Kadath::Domain_shell::change_basis_spher_to_cart	(	int	dd,
		const Tensor &	so
	)		const

virtual

Changes the tensorial basis from spherical to Cartesian in a given domain.

Parameters

dd	[input] : the domain. Should be consistent with *this.
so	[input] : the input tensor.

Returns: the tensor in Cartesian tensorial basis in the current domain.

Reimplemented from Kadath::Domain.

Definition at line 28 of file domain_shell_change_basis_tensor.cpp.

◆ connection_mtz()

Term_eq Kadath::Domain::connection_mtz ( const Term_eq & so ) const

virtualinherited

Computes the part of the gradient involving the connections, in spherical coordinates where the constant radius sections have negative curvature.

Parameters

so	: the input `Term_eq`

Returns: the result.

Definition at line 722 of file domain.cpp.

References Kadath::Term_eq::der_t, Kadath::Domain::div_r(), Kadath::Val_domain::div_sin_theta(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_space(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::indices(), Kadath::Domain::num_dom, Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Base_tensor::set_basis(), Kadath::Scalar::set_domain(), and Kadath::Term_eq::val_t.

◆ connection_spher()

Term_eq Kadath::Domain::connection_spher ( const Term_eq & so ) const

virtualinherited

Computes the part of the gradient involving the connections, in spherical orthonormal coordinates.

Parameters

so	: the input `Term_eq`

Returns: the result.

Reimplemented in Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 544 of file domain.cpp.

References Kadath::Term_eq::der_t, Kadath::Domain::div_r(), Kadath::Val_domain::div_sin_theta(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_space(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::indices(), Kadath::Val_domain::mult_cos_theta(), Kadath::Domain::num_dom, Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Base_tensor::set_basis(), Kadath::Scalar::set_domain(), and Kadath::Term_eq::val_t.

◆ ddp()

Val_domain Kadath::Domain_shell::ddp ( const Val_domain & so ) const

virtual

Compute the second derivative with respect to $\varphi$ of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the result.

Reimplemented from Kadath::Domain.

Definition at line 222 of file domain_shell_ope.cpp.

References Kadath::Val_domain::der_var().

◆ ddr()

Val_domain Kadath::Domain::ddr ( const Val_domain & so ) const

virtualinherited

Compute the second radial derivative w of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the result.

Definition at line 1452 of file domain.cpp.

References Kadath::Val_domain::der_r().

◆ ddt()

Val_domain Kadath::Domain::ddt ( const Val_domain & so ) const

virtualinherited

Compute the second derivative with respect to $\theta$ of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the result.

Reimplemented in Kadath::Domain_spheric_time_compact, Kadath::Domain_spheric_time_shell, and Kadath::Domain_spheric_time_nucleus.

Definition at line 1462 of file domain.cpp.

◆ ddtime()

Val_domain Kadath::Domain::ddtime ( const Val_domain & so ) const

virtualinherited

Computes the second time derivative of a field.

Parameters

so	[input] : the input field.

Returns: the result

Reimplemented in Kadath::Domain_spheric_periodic_compact, Kadath::Domain_spheric_periodic_shell, and Kadath::Domain_spheric_periodic_nucleus.

Definition at line 1480 of file domain.cpp.

◆ ddtime_term_eq()

Term_eq Kadath::Domain::ddtime_term_eq ( const Term_eq & so ) const

virtualinherited

Second time derivative of a Term_eq.

Parameters

so	: input field.

Returns: result.

Reimplemented in Kadath::Domain_polar_periodic_shell, and Kadath::Domain_polar_periodic_nucleus.

Definition at line 153 of file domain.cpp.

References Kadath::Domain::ddtime(), and Kadath::Domain::do_comp_by_comp().

◆ del_deriv()

void Kadath::Domain::del_deriv ( )

protectedvirtualinherited

Destroys the derivated members (like coloc, cart and radius), when changing the type of colocation points.

Reimplemented in Kadath::Domain_critic_outer, Kadath::Domain_critic_inner, Kadath::Domain_bispheric_eta_first, Kadath::Domain_bispheric_chi_first, Kadath::Domain_bispheric_rect, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 77 of file domain.cpp.

References Kadath::Domain::absol, Kadath::Domain::cart, Kadath::Domain::cart_surr, Kadath::Domain::coloc, Kadath::Domain::ndim, and Kadath::Domain::radius.

◆ der_harmonics_asym()

Term_eq Kadath::Domain_shell::der_harmonics_asym	(	const Term_eq &	so,
		const Term_eq &	omega,
		int	bound,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &)	f,
		const Param &	param,
		const Array< double > &	passage
	)		const

virtual

Fit, spherical harmonic by spherical harmonic, for the radial derivative of an anti-symmetric function.

Parameters

so	[input] : input scalar field.
omega	[input] : angular velocity.
bound	[input] : the boundary at which the computation is done.
f	[input] : pointer on the radial function describing the radial fit.
param	[input] : parameters of the radial fit.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the fit.

Reimplemented from Kadath::Domain.

Definition at line 363 of file multipoles_der.cpp.

References der_multipoles_asym(), der_radial_part_asym(), Kadath::Tensor::get_space(), Kadath::Domain::nbr_coefs, and Kadath::Term_eq::val_t.

◆ der_harmonics_sym()

Term_eq Kadath::Domain_shell::der_harmonics_sym	(	const Term_eq &	so,
		const Term_eq &	omega,
		int	bound,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &)	f,
		const Param &	param,
		const Array< double > &	passage
	)		const

virtual

Fit, spherical harmonic by spherical harmonic, for the radial derivative of a symmetric function.

Parameters

so	[input] : input scalar field.
omega	[input] : angular velocity.
bound	[input] : the boundary at which the computation is done.
f	[input] : pointer on the radial function describing the radial fit.
param	[input] : parameters of the radial fit.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the fit.

Reimplemented from Kadath::Domain.

Definition at line 320 of file multipoles_der.cpp.

References der_multipoles_sym(), der_radial_part_sym(), Kadath::Tensor::get_space(), Kadath::Domain::nbr_coefs, and Kadath::Term_eq::val_t.

◆ der_multipoles_asym()

Term_eq Kadath::Domain_shell::der_multipoles_asym	(	int	k,
		int	j,
		int	bound,
		const Term_eq &	so,
		const Array< double > &	passage
	)		const

virtual

Extraction of a given multipole, at some boundary, for the radial derivative of an anti-symmetric scalar function.

Parameters

k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
bound	[input] : the boundary at which the computation is done.
so	[input] : input scalar field.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the multipolar coefficient.

Reimplemented from Kadath::Domain.

Definition at line 146 of file multipoles_der.cpp.

References Kadath::Val_domain::allocate_conf(), Kadath::Val_domain::c, Kadath::Term_eq::der_t, Kadath::Array< T >::dimensions, Kadath::Domain::get_coloc(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Val_domain::set(), Kadath::Index::set(), Kadath::Val_domain::set_base(), Kadath::Scalar::set_domain(), Kadath::Val_domain::set_zero(), Kadath::Term_eq::type_data, val_boundary(), and Kadath::Term_eq::val_t.

◆ der_multipoles_sym()

Term_eq Kadath::Domain_shell::der_multipoles_sym	(	int	k,
		int	j,
		int	bound,
		const Term_eq &	so,
		const Array< double > &	passage
	)		const

virtual

Extraction of a given multipole, at some boundary, for the radial derivative a symmetric scalar function.

Parameters

k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
bound	[input] : the boundary at which the computation is done.
so	[input] : input scalar field.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the multipolar coefficient.

Reimplemented from Kadath::Domain.

Definition at line 32 of file multipoles_der.cpp.

References Kadath::Val_domain::allocate_conf(), Kadath::Val_domain::c, Kadath::Term_eq::der_t, Kadath::Array< T >::dimensions, Kadath::Domain::get_coloc(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Val_domain::set(), Kadath::Index::set(), Kadath::Val_domain::set_base(), Kadath::Scalar::set_domain(), Kadath::Val_domain::set_zero(), Kadath::Term_eq::type_data, val_boundary(), and Kadath::Term_eq::val_t.

◆ der_normal()

Val_domain Kadath::Domain_shell::der_normal	(	const Val_domain &	so,
		int	bound
	)		const

virtual

Normal derivative with respect to a given surface.

Parameters

so	: the input scalar field.
bound	: boundary at which the normal derivative is computed.

Returns: the normal derivative.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 74 of file domain_shell.cpp.

References alpha, and Kadath::Val_domain::der_var().

◆ der_normal_term_eq()

Term_eq Kadath::Domain::der_normal_term_eq	(	const Term_eq &	so,
		int	bound
	)		const

virtualinherited

Returns the normal derivative of a Term_eq.

Parameters

so	: input field.
bound	: the boundary.

Returns: the normal derivative.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 141 of file domain.cpp.

References Kadath::Domain::der_normal(), and Kadath::Domain::do_comp_by_comp_with_int().

◆ der_p()

Val_domain Kadath::Domain::der_p ( const Val_domain & so ) const

virtualinherited

Compute the derivative with respect to $\varphi$ of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the derivative.

Definition at line 1440 of file domain.cpp.

◆ der_partial_var()

Val_domain Kadath::Domain_shell::der_partial_var	(	const Val_domain &	so,
		int	ind
	)		const

virtual

Partial derivative with respect to a coordinate.

Parameters

so	: the input scalar field.
ind	: index of the variable used by the derivative.

Returns: the partial derivative.

Reimplemented from Kadath::Domain.

Definition at line 253 of file domain_shell_ope.cpp.

References Kadath::Val_domain::der_r(), and Kadath::Val_domain::der_var().

◆ der_r()

Val_domain Kadath::Domain_shell::der_r ( const Val_domain & so ) const

virtual

Compute the radial derivative of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the derivative.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 218 of file domain_shell_ope.cpp.

References alpha, and Kadath::Val_domain::der_var().

◆ der_r_rtwo()

Val_domain Kadath::Domain::der_r_rtwo ( const Val_domain & so ) const

virtualinherited

Compute the radial derivative multiplied by of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the result.

Reimplemented in Kadath::Domain_compact_symphi, Kadath::Domain_compact, and Kadath::Domain_polar_compact.

Definition at line 1446 of file domain.cpp.

◆ der_radial_part_asym()

Term_eq Kadath::Domain_shell::der_radial_part_asym	(	const Space &	space,
		int	k,
		int	j,
		const Term_eq &	omega,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &)	f,
		const Param &	param
	)		const

virtual

Gives some radial fit for a given multipole, intended for the radial derivative of an anti-symmetric scalar function.

Parameters

space	[input] : the concerned `Space`.
k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
omega	[input] : angular velocity.
f	[input] : pointer on the radial function describing the fit.
param	[input] : parameters of the radial fit.

Returns: the radial fit.

Reimplemented from Kadath::Domain.

Definition at line 289 of file multipoles_der.cpp.

References Kadath::Term_eq::der_t, Kadath::Term_eq::get_der_t(), Kadath::Term_eq::get_dom(), Kadath::Term_eq::get_val_t(), Kadath::Domain::nbr_coefs, Kadath::Term_eq::type_data, and val_boundary().

◆ der_radial_part_sym()

Term_eq Kadath::Domain_shell::der_radial_part_sym	(	const Space &	space,
		int	k,
		int	j,
		const Term_eq &	omega,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &param)	f,
		const Param &	param
	)		const

virtual

Gives some radial fit for a given multipole, intended for the radial derivative of a symmetric scalar function.

Parameters

space	[input] : the concerned `Space`.
k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
omega	[input] : angular velocity.
f	[input] : pointer on the radial function describing the fit.
param	[input] : parameters of the radial fit.

Returns: the radial fit.

Reimplemented from Kadath::Domain.

Definition at line 259 of file multipoles_der.cpp.

References Kadath::Term_eq::der_t, Kadath::Term_eq::get_der_t(), Kadath::Term_eq::get_dom(), Kadath::Term_eq::get_val_t(), Kadath::Domain::nbr_coefs, Kadath::Term_eq::type_data, and val_boundary().

◆ der_t()

Val_domain Kadath::Domain::der_t ( const Val_domain & so ) const

virtualinherited

Compute the derivative with respect to $\theta$ of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the derivative.

Definition at line 1435 of file domain.cpp.

◆ derive_flat_cart()

Term_eq Kadath::Domain_shell::derive_flat_cart	(	int	tipe,
		char	ind,
		const Term_eq &	so,
		const Metric *	manip
	)		const

virtual

Computes the flat derivative of a Term_eq, in Cartesian coordinates.

If the index of the derivative is present in the source, appropriate contraction is performed. If the contravariant version is called for, the index is raised using an arbitrary metric.

Parameters

tipe	: type of derivative (`COV` or `CON`)
ind	: name of the index corresponding to the derivative.
so	: input field.
manip	: pointer on the metric used to manipulate the derivative index, if need be.

Returns: result.

Reimplemented from Kadath::Domain.

Definition at line 299 of file domain_shell_for_metric.cpp.

References Kadath::Term_eq::der_t, Kadath::Tensor::do_summation_one_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_name_ind(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::is_name_affected(), Kadath::Metric::manipulate_ind(), Kadath::Domain::num_dom, Kadath::Metric::p_met_con, Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Scalar::set_domain(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_flat_mtz()

Term_eq Kadath::Domain_shell::derive_flat_mtz	(	int	tipe,
		char	ind,
		const Term_eq &	so,
		const Metric *	manip
	)		const

virtual

Computes the flat derivative of a Term_eq, in spherical coordinates where the constant radii sections have a negative curvature.

If the index of the derivative is present in the source, appropriate contraction is performed. If the contravariant version is called for, the index is raised using an arbitrary metric.

Parameters

tipe	: type of derivative (`COV` or `CON`)
ind	: name of the index corresponding to the derivative.
so	: input field.
manip	: pointer on the metric used to manipulate the derivative index, if need be.

Returns: result.

Reimplemented from Kadath::Domain.

Definition at line 395 of file domain_shell_for_metric.cpp.

◆ derive_flat_spher()

Term_eq Kadath::Domain_shell::derive_flat_spher	(	int	tipe,
		char	ind,
		const Term_eq &	so,
		const Metric *	manip
	)		const

virtual

Computes the flat derivative of a Term_eq, in spherical orthonormal coordinates.

If the index of the derivative is present in the source, appropriate contraction is performed. If the contravariant version is called for, the index is raised using an arbitrary metric.

Parameters

tipe	: type of derivative (`COV` or `CON`)
ind	: name of the index corresponding to the derivative.
so	: input field.
manip	: pointer on the metric used to manipulate the derivative index, if need be.

Returns: result.

Reimplemented from Kadath::Domain.

Definition at line 30 of file domain_shell_for_metric.cpp.

◆ div_1mrsL()

Val_domain Kadath::Domain_shell::div_1mrsL ( const Val_domain & so ) const

virtual

Division by .

Parameters

so	: the input

Returns: the output

Reimplemented from Kadath::Domain.

Definition at line 176 of file domain_shell_ope.cpp.

References alpha, Kadath::Val_domain::base, beta, Kadath::Val_domain::cf, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ div_1mx2()

Val_domain Kadath::Domain_shell::div_1mx2 ( const Val_domain & ) const

virtual

Division by .

Reimplemented from Kadath::Domain.

Definition at line 200 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ div_1mx2_term_eq()

Term_eq Kadath::Domain::div_1mx2_term_eq ( const Term_eq & so ) const

virtualinherited

Returns the division by of a Term_eq.

Parameters

so	: input field.

Returns: the result of the division.

Definition at line 1765 of file domain.cpp.

References Kadath::Domain::div_1mx2(), and Kadath::Domain::do_comp_by_comp().

◆ div_chi()

Val_domain Kadath::Domain::div_chi ( const Val_domain & ) const

virtualinherited

Division by $\chi$ .

Reimplemented in Kadath::Domain_bispheric_eta_first, Kadath::Domain_bispheric_chi_first, and Kadath::Domain_bispheric_rect.

Definition at line 1351 of file domain.cpp.

◆ div_cos_theta()

Val_domain Kadath::Domain_shell::div_cos_theta ( const Val_domain & ) const

virtual

Division by $\cos \theta$ .

Reimplemented from Kadath::Domain.

Definition at line 145 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ div_r()

Val_domain Kadath::Domain_shell::div_r ( const Val_domain & so ) const

virtual

Division by .

Parameters

so	: the input

Returns: the output

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 212 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, and Kadath::Domain::get_radius().

◆ div_r_term_eq()

Term_eq Kadath::Domain::div_r_term_eq ( const Term_eq & so ) const

virtualinherited

Division by $r$ of a Term_eq.

Parameters

so	: input field.

Returns: result.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, and Kadath::Domain_polar_shell_inner_adapted.

Definition at line 169 of file domain.cpp.

References Kadath::Domain::div_r(), and Kadath::Domain::do_comp_by_comp().

◆ div_sin_chi()

Val_domain Kadath::Domain::div_sin_chi ( const Val_domain & ) const

virtualinherited

Division by $\sin \chi$ .

Reimplemented in Kadath::Domain_bispheric_eta_first, Kadath::Domain_bispheric_chi_first, and Kadath::Domain_bispheric_rect.

Definition at line 1345 of file domain.cpp.

◆ div_sin_theta()

Val_domain Kadath::Domain_shell::div_sin_theta ( const Val_domain & ) const

virtual

Division by $\sin \theta$ .

Reimplemented from Kadath::Domain.

Definition at line 134 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ div_x()

Val_domain Kadath::Domain::div_x ( const Val_domain & ) const

virtualinherited

Division by .

Reimplemented in Kadath::Domain_spheric_time_nucleus, Kadath::Domain_nucleus_symphi, Kadath::Domain_spheric_periodic_nucleus, Kadath::Domain_nucleus, Kadath::Domain_polar_periodic_nucleus, Kadath::Domain_polar_nucleus, Kadath::Domain_fourD_periodic_nucleus, and Kadath::Domain_critic_inner.

Definition at line 1260 of file domain.cpp.

◆ div_xm1()

Val_domain Kadath::Domain_shell::div_xm1 ( const Val_domain & ) const

virtual

Division by .

Reimplemented from Kadath::Domain.

Definition at line 237 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ div_xp1()

Val_domain Kadath::Domain_shell::div_xp1 ( const Val_domain & ) const

virtual

Division by .

Reimplemented from Kadath::Domain.

Definition at line 189 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ do_absol()

void Kadath::Domain_shell::do_absol ( ) const

privatevirtual

Computes the absolute coordinates.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 92 of file domain_shell.cpp.

References Kadath::Domain::absol, alpha, beta, center, Kadath::Domain::coloc, Kadath::Index::inc(), and Kadath::Domain::nbr_points.

◆ do_cart()

void Kadath::Domain_shell::do_cart ( ) const

privatevirtual

Computes the Cartesian coordinates.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 127 of file domain_shell.cpp.

References alpha, beta, Kadath::Domain::cart, center, Kadath::Domain::coloc, Kadath::Index::inc(), and Kadath::Domain::nbr_points.

◆ do_cart_surr()

void Kadath::Domain_shell::do_cart_surr ( ) const

privatevirtual

Computes the Cartesian coordinates over the radius.

Reimplemented from Kadath::Domain.

Definition at line 149 of file domain_shell.cpp.

References Kadath::Domain::cart_surr, Kadath::Domain::coloc, Kadath::Index::inc(), and Kadath::Domain::nbr_points.

◆ do_coloc()

void Kadath::Domain_shell::do_coloc ( )

privatevirtual

Computes the colocation points.

Reimplemented from Kadath::Domain.

Definition at line 252 of file domain_shell.cpp.

References Kadath::Domain::coloc, Kadath::Domain::del_deriv(), Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Domain::ndim, Kadath::Dim_array::set(), and Kadath::Domain::type_base.

◆ do_comp_by_comp()

Term_eq Kadath::Domain::do_comp_by_comp	(	const Term_eq &	so,
		Val_domain(Domain::*)(const Val_domain &) const	pfunc
	)		const

protectedinherited

Function used to apply the same operation to all the components of a tensor, in the current domain.

It works at the Term_eq level and the same operation is applied to both the value and the variation of the tensor.

Parameters

so	: the source tensor.
pfunc	: pointer onf the function to be applied.

Returns: the resulting Term_eq.

Definition at line 283 of file domain.cpp.

◆ do_comp_by_comp_with_int()

Term_eq Kadath::Domain::do_comp_by_comp_with_int	(	const Term_eq &	so,
		int	val,
		Val_domain(Domain::*)(const Val_domain &, int) const	pfunc
	)		const

protectedinherited

Function used to apply the same operation to all the components of a tensor, in the current domain.

The operation applied depends on an integer parameter. It works at the Term_eq level and the same operation is applied to both the value and the variation of the tensor.

Parameters

so	: the source tensor.
val	: the integer parameter.
pfunc	: pointer onf the function to be applied.

Returns: the resulting Term_eq.

Definition at line 228 of file domain.cpp.

◆ do_der_abs_from_der_var()

void Kadath::Domain_shell::do_der_abs_from_der_var	(	const Val_domain const const	der_var,
		Val_domain **const	der_abs
	)		const

virtual

Computes the derivative with respect to the absolute Cartesian coordinates from the derivative with respect to the numerical coordinates.

$\displaystyle\frac{\partial f}{\partial X} = (\sin\theta \displaystyle\frac{\partial f}{\alpha\partial x} + \cos\theta \displaystyle\frac{\partial f}{r\partial \theta^\star}) \cos\varphi - \sin\varphi \displaystyle\frac{\partial f}{r\sin\theta \partial \varphi^\star}$
$\displaystyle\frac{\partial f}{\partial Y} = (\sin\theta \displaystyle\frac{\partial f}{\alpha\partial x} + \cos\theta \displaystyle\frac{\partial f}{r\partial \theta^\star}) \sin\varphi + \cos\varphi \displaystyle\frac{\partial f}{r\sin\theta \partial \varphi^\star}$
$\displaystyle\frac{\partial f}{\partial Z} = \cos\theta \displaystyle\frac{\partial f}{\alpha\partial x} - \sin\theta\displaystyle\frac{\partial f}{r\partial \theta^\star}$
Parameters

der_var [input] : the ndim derivatives with respect to the numerical coordinates.

der_abs [output] : the ndim derivatives with respect to the absolute Cartesian coordinates.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 705 of file domain_shell.cpp.

References alpha, Kadath::Val_domain::div_sin_theta(), Kadath::Val_domain::get_base(), Kadath::Domain::get_radius(), Kadath::Val_domain::mult_cos_phi(), mult_cos_phi(), Kadath::Val_domain::mult_cos_theta(), mult_cos_theta(), Kadath::Val_domain::mult_sin_phi(), mult_sin_phi(), Kadath::Val_domain::mult_sin_theta(), mult_sin_theta(), and Kadath::Val_domain::set_base().

◆ do_radius()

void Kadath::Domain_shell::do_radius ( ) const

privatevirtual

Computes the generalized radius.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 114 of file domain_shell.cpp.

References Kadath::Val_domain::allocate_conf(), alpha, beta, Kadath::Domain::coloc, Kadath::Index::inc(), Kadath::Domain::nbr_points, Kadath::Domain::radius, and Kadath::Val_domain::set().

◆ do_which_points_boundary()

void Kadath::Domain_shell::do_which_points_boundary	(	int	bound,
		const Base_spectral &	base,
		Index **	ind,
		int	start
	)		const

virtual

Lists all the indices corresponding to true collocation points on a boundary.

Parameters

bound	the boundary.
base	: the spect basis. Its symmetries are used to get the right result.
ind	: the list of indices.
start	: states where the indices are stored in ind. The first is in ind[start]

Reimplemented from Kadath::Domain.

Definition at line 90 of file domain_shell_systems.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Domain::nbr_points, and Kadath::Index::set().

◆ dr_term_eq()

Term_eq Kadath::Domain::dr_term_eq ( const Term_eq & so ) const

virtualinherited

Radial derivative of a Term_eq.

Parameters

so	: input field.

Returns: result.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 145 of file domain.cpp.

References Kadath::Domain::der_r(), and Kadath::Domain::do_comp_by_comp().

◆ dt()

Val_domain Kadath::Domain_shell::dt ( const Val_domain & so ) const

virtual

Compute the derivative with respect to $\theta$ of a scalar field.

Parameters

so	[input] : the input scalar field.

Returns: the result.

Reimplemented from Kadath::Domain.

Definition at line 248 of file domain_shell_ope.cpp.

References Kadath::Val_domain::der_var().

◆ dtime()

Val_domain Kadath::Domain::dtime ( const Val_domain & so ) const

virtualinherited

Computes the time derivative of a field.

Parameters

so	[input] : the input field.

Returns: the result.

Reimplemented in Kadath::Domain_spheric_periodic_compact, Kadath::Domain_spheric_periodic_shell, Kadath::Domain_spheric_periodic_nucleus, Kadath::Domain_polar_periodic_shell, and Kadath::Domain_polar_periodic_nucleus.

Definition at line 1474 of file domain.cpp.

◆ dtime_term_eq()

Term_eq Kadath::Domain::dtime_term_eq ( const Term_eq & so ) const

virtualinherited

Time derivative of a Term_eq.

Parameters

so	: input field.

Returns: result.

Reimplemented in Kadath::Domain_polar_periodic_shell, and Kadath::Domain_polar_periodic_nucleus.

Definition at line 149 of file domain.cpp.

References Kadath::Domain::do_comp_by_comp(), and Kadath::Domain::dtime().

◆ export_tau()

void Kadath::Domain_shell::export_tau	(	const Tensor &	eq,
		int	dom,
		int	order,
		Array< double > &	res,
		int &	pos_res,
		const Array< int > &	ncond,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtual

Exports all the residual equations corresponding to a tensorial one in the bulk.

It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
order	: describes the order of the equation (2 for a Laplacian for instance).
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: `Array` containing the number of equations corresponding to each component. It is used when some of the components are null.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Reimplemented from Kadath::Domain.

Definition at line 212 of file domain_shell_export_tau.cpp.

References export_tau_val_domain(), export_tau_val_domain_mquant(), Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Param_tensor::get_m_order(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_m_order_affected(), and Kadath::Tensor::is_m_quant_affected().

◆ export_tau_array()

void Kadath::Domain::export_tau_array	(	const Tensor &	eq,
		int	dom,
		const Array< int > &	order,
		Array< double > &	res,
		int &	pos_res,
		const Array< int > &	ncond,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtualinherited

Exports all the residual equations corresponding to one tensorial one in the bulk.

It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
order	: describes the order of the equation, with respect to each variable.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: `Array` containing the number of equations corresponding to each component. It is used when some of the components are null.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Reimplemented in Kadath::Domain_spheric_time_compact, Kadath::Domain_spheric_time_shell, and Kadath::Domain_spheric_time_nucleus.

Definition at line 1539 of file domain.cpp.

◆ export_tau_boundary()

void Kadath::Domain_shell::export_tau_boundary	(	const Tensor &	eq,
		int	dom,
		int	bound,
		Array< double > &	res,
		int &	pos_res,
		const Array< int > &	ncond,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtual

Exports all the residual equations corresponding to a tensorial one on a given boundary It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
bound	: the boundary at which the equation is enforced.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: `Array` containing the number of equations corresponding to each component. It is used when some of the components are null.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Reimplemented from Kadath::Domain.

Definition at line 200 of file domain_shell_export_tau_boundary.cpp.

References export_tau_val_domain_boundary(), export_tau_val_domain_boundary_mquant(), Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Param_tensor::get_m_order(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_m_order_affected(), and Kadath::Tensor::is_m_quant_affected().

◆ export_tau_boundary_array()

void Kadath::Domain::export_tau_boundary_array	(	const Tensor &	eq,
		int	dom,
		int	bound,
		const Array< int > &	order,
		Array< double > &	res,
		int &	pos_res,
		const Array< int > &	ncond,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtualinherited

Exports all the residual equations corresponding to one tensorial one on a given boundary It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
bound	: the boundary at which the equation is enforced.
order	: describes the order of the equation, with respect to each variable. The one normal to the surface is irrelevant.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: `Array` containing the number of equations corresponding to each component. It is used when some of the components are null.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Reimplemented in Kadath::Domain_spheric_time_compact, Kadath::Domain_spheric_time_shell, and Kadath::Domain_spheric_time_nucleus.

Definition at line 1557 of file domain.cpp.

◆ export_tau_boundary_exception()

void Kadath::Domain_shell::export_tau_boundary_exception	(	const Tensor &	eq,
		int	dom,
		int	bound,
		Array< double > &	res,
		int &	pos_res,
		const Array< int > &	ncond,
		const Param &	param,
		int	type_exception,
		const Tensor &	exception,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtual

Exports all the residual equations corresponding to one tensorial one on a given boundary, excepted for some coefficients where another equation is used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
bound	: the boundary at which the equation is enforced.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: `Array` containing the number of equations corresponding to each component. It is used when some of the components are null.
param	: parameters describing the coefficients where the alternative condition is enforced.
type_exception	: states which type of exception (value or derivative ; current domain or the other one). Highly specialized...
exception	: the equation used for the alternative condition.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Returns: the number of true conditions.

Reimplemented from Kadath::Domain.

Definition at line 550 of file domain_shell_export_tau_boundary_exception.cpp.

References export_tau_val_domain_boundary_exception(), export_tau_val_domain_boundary_exception_mquant(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_valence(), and Kadath::Tensor::is_m_quant_affected().

◆ export_tau_boundary_one_side()

void Kadath::Domain::export_tau_boundary_one_side	(	const Tensor &	eq,
		int	dom,
		int	bound,
		Array< double > &	res,
		int &	pos_res,
		const Array< int > &	ncond,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtualinherited

Exports all the residual equations corresponding to one tensorial one on a given boundary.

The boundary is assumed to also have boundaries. (Used for bispherical coordinates). It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
bound	: the boundary at which the equation is enforced.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: `Array` containing the number of equations corresponding to each component. It is used when some of the components are null.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Reimplemented in Kadath::Domain_bispheric_eta_first, Kadath::Domain_bispheric_chi_first, and Kadath::Domain_bispheric_rect.

Definition at line 1563 of file domain.cpp.

◆ export_tau_val_domain()

void Kadath::Domain_shell::export_tau_val_domain	(	const Val_domain &	eq,
		int	mlim,
		int	order,
		Array< double > &	res,
		int &	pos_res,
		int	ncond
	)		const

Exports a residual equation in the bulk.

It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
mlim	: limit for the regularity .
order	: describes the order of the equation (2 for a Laplacian for instance).
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: the corresponding number of equations. It is used when the equation is null.

Definition at line 117 of file domain_shell_export_tau.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_base(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), and Kadath::Index::set().

◆ export_tau_val_domain_boundary()

void Kadath::Domain_shell::export_tau_val_domain_boundary	(	const Val_domain &	eq,
		int	mlim,
		int	bound,
		Array< double > &	res,
		int &	pos_res,
		int	ncond
	)		const

Exports all the residual equations corresponding to a tensorial one on a given boundary It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
mlim	: limit for the regularity.
bound	: the boundary at which the equation is enforced.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: the corresponding number of equations. It is used when the residual is null.

Definition at line 109 of file domain_shell_export_tau_boundary.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_base(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), Kadath::Index::set(), and val_boundary().

◆ export_tau_val_domain_boundary_exception()

void Kadath::Domain_shell::export_tau_val_domain_boundary_exception	(	const Val_domain &	eq,
		int	mlim,
		int	bound,
		Array< double > &	res,
		int &	pos_res,
		int	ncond,
		const Param &	param,
		int	type_exception,
		const Val_domain &	exception
	)		const

Exports all the residual equations corresponding to one tensorial one on a given boundary, excepted for some coefficients where another equation is used.

Parameters

eq	: the residual of the equation.
mlim	: limit for the regularity.
bound	: the boundary at which the equation is enforced.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: the corresponding number of equations. It is used when the equation is null.
param	: parameters describing the coefficients where the alternative condition is enforced.
type_exception	: states which type of exception (value or derivative ; current domain or the other one). Highly specialized...
exception	: the equation used for the alternative condition.

Returns: the number of true conditions.

Definition at line 287 of file domain_shell_export_tau_boundary_exception.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_base(), Kadath::Param::get_double(), Kadath::Param::get_int(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), Kadath::Index::set(), and val_boundary().

◆ export_tau_val_domain_boundary_exception_mquant()

void Kadath::Domain_shell::export_tau_val_domain_boundary_exception_mquant	(	const Val_domain &	eq,
		int	mquant,
		int	bound,
		Array< double > &	res,
		int &	pos_res,
		int	ncond,
		const Param &	param,
		int	type_exception,
		const Val_domain &	exception
	)		const

Exports all the residual equations corresponding to one tensorial one on a given boundary, excepted for some coefficients where another equation is used.

Parameters

eq	: the residual of the equation.
mquant	: quantum number wrt $\varphi$ .
bound	: the boundary at which the equation is enforced.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: the corresponding number of equations. It is used when the equation is null.
param	: parameters describing the coefficients where the alternative condition is enforced.
type_exception	: states which type of exception (value or derivative ; current domain or the other one). Highly specialized...
exception	: the equation used for the alternative condition.

Returns: the number of true conditions.

Definition at line 30 of file domain_shell_export_tau_boundary_exception.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_base(), Kadath::Param::get_double(), Kadath::Param::get_int(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), Kadath::Index::set(), and val_boundary().

◆ export_tau_val_domain_boundary_mquant()

void Kadath::Domain_shell::export_tau_val_domain_boundary_mquant	(	const Val_domain &	eq,
		int	mquant,
		int	bound,
		Array< double > &	res,
		int &	pos_res,
		int	ncond
	)		const

Exports all the residual equations corresponding to a tensorial one on a given boundary It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
mquant	: quantum number wrt $\varphi$ .
bound	: the boundary at which the equation is enforced.
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: the corresponding number of equations. It is used when the residual is null.

Definition at line 29 of file domain_shell_export_tau_boundary.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_base(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), Kadath::Index::set(), and val_boundary().

◆ export_tau_val_domain_mquant()

void Kadath::Domain_shell::export_tau_val_domain_mquant	(	const Val_domain &	eq,
		int	mquant,
		int	order,
		Array< double > &	res,
		int &	pos_res,
		int	ncond
	)		const

Exports a residual equation in the bulk.

It makes use of the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
mquant	: quantum number wrt $\varphi$ .
order	: describes the order of the equation (2 for a Laplacian for instance).
res	: The `Array` where the discretized equations are stored.
pos_res	: current position in res.
ncond	: the corresponding number of equations. It is used when the equation is null.

Definition at line 29 of file domain_shell_export_tau.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_base(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), and Kadath::Index::set().

◆ filter()

void Kadath::Domain::filter	(	Tensor &	tt,
		int	dom,
		double	treshold
	)		const

virtualinherited

Puts to zero all the coefficients below a given treshold.

Regularity is maintained by dealing properly with the various Galerkin basis

Parameters

tt	: the `Tensor` to be filtered.
dom	: the domain considered (should be the same as num_dom).
treshold	: all coefficients below this are set to zero.

Reimplemented in Kadath::Domain_nucleus_symphi.

Definition at line 1759 of file domain.cpp.

◆ find_other_dom()

void Kadath::Domain_shell::find_other_dom	(	int	dom,
		int	bound,
		int &	otherdom,
		int &	otherbound
	)		const

virtual

Gives the informations corresponding the a touching neighboring domain.

Parameters

dom	: index of the currect domain (deprecated, should be the same as num_dom)
bound	: the boundary between the two domains.
otherdom	: index of the other domain.
otherbound	: name of the boundary, as seen by the other domain.

Reimplemented from Kadath::Domain.

Definition at line 26 of file domain_shell_systems.cpp.

◆ fitschwarz() [1/2]

Term_eq Kadath::Domain_shell::fitschwarz	(	const Term_eq &	so,
		int	dim
	)		const

Fit some field with a decay (Term_eq version).

Parameters

so	: the field to be fitted.
dim	: the dimension.

Returns: : the fit.

Definition at line 62 of file fitschwarz_shell.cpp.

References Kadath::Val_domain::check_if_zero(), fitschwarz(), Kadath::Term_eq::get_der_t(), Kadath::Term_eq::get_dom(), Kadath::Space::get_domain(), Kadath::Term_eq::get_p_der_t(), Kadath::Tensor::get_space(), Kadath::Term_eq::get_type_data(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::indices(), Kadath::Tensor::set(), Kadath::Scalar::set_domain(), and Kadath::Val_domain::set_zero().

◆ fitschwarz() [2/2]

Val_domain Kadath::Domain_shell::fitschwarz	(	const Val_domain &	so,
		int	dim
	)		const

Fit some field with a decay (Val_domain version).

Parameters

so	: the field to be fitted.
dim	: the dimension.

Returns: : the fit.

Definition at line 29 of file fitschwarz_shell.cpp.

References Kadath::Val_domain::allocate_coef(), alpha, Kadath::Val_domain::base, beta, Kadath::Val_domain::coef(), der_normal(), Kadath::Val_domain::get_coef(), Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Val_domain::set_coef().

◆ get_absol()

Val_domain const & Kadath::Domain::get_absol ( int i ) const

inlineinherited

Returns the absolute coordinates.

Definition at line 1457 of file space.hpp.

References Kadath::Domain::absol, Kadath::Domain::do_absol(), and Kadath::Domain::ndim.

◆ get_cart()

Val_domain const & Kadath::Domain::get_cart ( int i ) const

inlineinherited

Returns a Cartesian coordinates.

Parameters

i	[input] : composant ( $0 \leq i <$ `ndim`).

Definition at line 1471 of file space.hpp.

References Kadath::Domain::cart, Kadath::Domain::do_cart(), and Kadath::Domain::ndim.

◆ get_cart_surr()

Val_domain const & Kadath::Domain::get_cart_surr ( int i ) const

inlineinherited

Returns a Cartesian coordinates divided by the radius.

Parameters

i	[input] : composant ( $0 \leq i <$ `ndim`).

Definition at line 1479 of file space.hpp.

References Kadath::Domain::cart_surr, Kadath::Domain::do_cart_surr(), and Kadath::Domain::ndim.

◆ get_center()

virtual Point Kadath::Domain_shell::get_center ( ) const

inlinevirtual

Returns the center.

Reimplemented from Kadath::Domain.

Definition at line 664 of file spheric.hpp.

References center.

◆ get_chi()

const Val_domain & Kadath::Domain::get_chi ( ) const

virtualinherited

Returns the variable $\chi$ .

Reimplemented in Kadath::Domain_bispheric_eta_first, Kadath::Domain_bispheric_chi_first, and Kadath::Domain_bispheric_rect.

Definition at line 1387 of file domain.cpp.

◆ get_coloc()

Array< double > const & Kadath::Domain::get_coloc ( int i ) const

inlineinherited

Returns the colocation points for a given variable.

Definition at line 1486 of file space.hpp.

References Kadath::Domain::coloc, and Kadath::Domain::ndim.

◆ get_eta()

const Val_domain & Kadath::Domain::get_eta ( ) const

virtualinherited

Returns the variable $\eta$ .

Reimplemented in Kadath::Domain_bispheric_eta_first, Kadath::Domain_bispheric_chi_first, and Kadath::Domain_bispheric_rect.

Definition at line 1393 of file domain.cpp.

◆ get_nbr_coefs()

Dim_array const& Kadath::Domain::get_nbr_coefs ( ) const

inlineinherited

Returns the number of coefficients.

Definition at line 94 of file space.hpp.

References Kadath::Domain::nbr_coefs.

◆ get_nbr_points()

Dim_array const& Kadath::Domain::get_nbr_points ( ) const

inlineinherited

Returns the number of points.

Definition at line 92 of file space.hpp.

References Kadath::Domain::nbr_points.

◆ get_ndim()

int Kadath::Domain::get_ndim ( ) const

inlineinherited

Returns the number of dimensions.

Definition at line 96 of file space.hpp.

References Kadath::Domain::ndim.

◆ get_num()

int Kadath::Domain::get_num ( ) const

inlineinherited

Returns the index of the curent domain.

Definition at line 90 of file space.hpp.

References Kadath::Domain::num_dom.

◆ get_radius()

Val_domain const & Kadath::Domain::get_radius ( ) const

inlineinherited

Returns the generalized radius.

Definition at line 1465 of file space.hpp.

References Kadath::Domain::do_radius(), and Kadath::Domain::radius.

◆ get_rmax()

virtual double Kadath::Domain_shell::get_rmax ( ) const

inlinevirtual

Returns the maximum radius.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 662 of file spheric.hpp.

References alpha, and beta.

◆ get_rmin()

virtual double Kadath::Domain_shell::get_rmin ( ) const

inlinevirtual

Returns the minimum radius.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 661 of file spheric.hpp.

References alpha, and beta.

◆ get_T()

const Val_domain & Kadath::Domain::get_T ( ) const

virtualinherited

Returns the variable .

Reimplemented in Kadath::Domain_critic_outer, and Kadath::Domain_critic_inner.

Definition at line 1405 of file domain.cpp.

◆ get_type_base()

int Kadath::Domain::get_type_base ( ) const

inlineinherited

Returns the type of the basis.

Definition at line 98 of file space.hpp.

References Kadath::Domain::type_base.

◆ get_X()

const Val_domain & Kadath::Domain::get_X ( ) const

virtualinherited

Returns the variable .

Reimplemented in Kadath::Domain_critic_outer, and Kadath::Domain_critic_inner.

Definition at line 1399 of file domain.cpp.

◆ give_normal()

const Term_eq * Kadath::Domain::give_normal	(	int	bound,
		int	tipe
	)		const

virtualinherited

Returns the vector normal to a surface.

Must be a Term_eq because the dmain can be a variable one.

Parameters

bound	[input] : the boundary where the normal is computed.
tipe	[input] : tensorial coordinates used. (Cartesian or spherical basis)

Returns: the normal derivative.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 1715 of file domain.cpp.

◆ give_place_var()

int Kadath::Domain_shell::give_place_var ( char * name ) const

privatevirtual

Translates a name of a coordinate into its corresponding numerical name.

Parameters

name	: name of the variable (like 'R', for the radius).

Returns: the corresponding number (1 for 'R' for instance). The result is -1 if the name is not recognized.

Reimplemented from Kadath::Domain.

Definition at line 891 of file domain_shell.cpp.

◆ grad_term_eq()

Term_eq Kadath::Domain::grad_term_eq ( const Term_eq & so ) const

virtualinherited

Gradient of Term_eq.

Parameters

so	: input field.

Returns: result.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, and Kadath::Domain_polar_shell_inner_adapted.

Definition at line 173 of file domain.cpp.

References Kadath::Term_eq::der_t, Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_parameters(), Kadath::Tensor::is_m_quant_affected(), Kadath::Domain::partial_cart(), Kadath::Param_tensor::set_m_quant(), Kadath::Tensor::set_parameters(), and Kadath::Term_eq::val_t.

◆ harmonics_asym()

Term_eq Kadath::Domain_shell::harmonics_asym	(	const Term_eq &	so,
		const Term_eq &	omega,
		int	bound,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &)	f,
		const Param &	param,
		const Array< double > &	passage
	)		const

virtual

Fit, spherical harmonic by spherical harmonic, for an anti-symmetric function.

Parameters

so	[input] : input scalar field.
omega	[input] : angular velocity.
bound	[input] : the boundary at which the computation is done.
f	[input] : pointer on the radial function describing the radial fit.
param	[input] : parameters of the radial fit.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the fit.

Reimplemented from Kadath::Domain.

Definition at line 579 of file multipoles.cpp.

References Kadath::Tensor::get_space(), multipoles_asym(), Kadath::Domain::nbr_coefs, radial_part_asym(), and Kadath::Term_eq::val_t.

◆ harmonics_sym()

Term_eq Kadath::Domain_shell::harmonics_sym	(	const Term_eq &	so,
		const Term_eq &	omega,
		int	bound,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &)	f,
		const Param &	param,
		const Array< double > &	passage
	)		const

virtual

Fit, spherical harmonic by spherical harmonic, for a symmetric function.

Parameters

so	[input] : input scalar field.
omega	[input] : angular velocity.
bound	[input] : the boundary at which the computation is done.
f	[input] : pointer on the radial function describing the radial fit.
param	[input] : parameters of the radial fit.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the fit.

Reimplemented from Kadath::Domain.

Definition at line 539 of file multipoles.cpp.

References Kadath::Tensor::get_space(), multipoles_sym(), Kadath::Domain::nbr_coefs, radial_part_sym(), and Kadath::Term_eq::val_t.

◆ import() [1/2]

Term_eq Kadath::Domain::import	(	int	numdom,
		int	bound,
		int	n_ope,
		Term_eq **	parts
	)		const

inherited

Gets the value of a Term_eq by importing data from neighboring domains, on a boundary.

This makes use of the spectral summation.

Parameters

numdom	: the domain considered (should be the same as num_dom).
bound	: the boundary where the values from the other domains are computed.
n_ope	: number of other domains touching the current one at the given boundary.
parts	: pointers on the various `Term_eq` that have to be imported.

Returns: the imported field. Assumed to be constant in the direction normal to the boundary.

Definition at line 107 of file domain.cpp.

References Kadath::Domain::der_t(), Kadath::Term_eq::get_dom(), and Kadath::Array< T >::set().

◆ import() [2/2]

Tensor Kadath::Domain_shell::import	(	int	numdom,
		int	bound,
		int	n_ope,
		const Array< int > &	other_doms,
		Tensor **	parts
	)		const

virtual

Gets the value of a Tensor by importing data from neighboring domains, on a boundary.

This makes use of the spectral summation.

Parameters

numdom	: the domain considered (should be the same as num_dom).
bound	: the boundary where the values from the other domains are computed.
n_ope	: number of other domains touching the current one at the given boundary.
other_doms	: numbers of the other pertinent domains.
parts	: pointers on the various `Tensors` that have to be imported.

Returns: the imported field. Assumed to be constant in the direction normal to the boundary.

Reimplemented from Kadath::Domain.

Definition at line 30 of file domain_shell_import.cpp.

References absol_to_num(), Kadath::Tensor::cmp, Kadath::Tensor::coef(), Kadath::Domain::get_cart(), Kadath::Tensor::get_n_comp(), Kadath::Domain::get_nbr_points(), is_in(), Kadath::Domain::nbr_points, Kadath::Index::set(), Kadath::Point::set(), Kadath::Tensor::set_basis(), and Kadath::Tensor::std_base().

◆ integ()

double Kadath::Domain_shell::integ	(	const Val_domain &	so,
		int	bound
	)		const

virtual

Surface integral on a given boundary.

Parameters

so	: the input scalar field.
bound	: boundary at which the integral is computed.

Returns: the surface integral.

Reimplemented from Kadath::Domain.

Definition at line 902 of file domain_shell.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::get_base(), mult_r(), mult_sin_theta(), Kadath::Domain::nbr_coefs, Kadath::Index::set(), and val_boundary().

◆ integ_term_eq()

Term_eq Kadath::Domain::integ_term_eq	(	const Term_eq &	so,
		int	bound
	)		const

virtualinherited

Surface integral of a Term_eq.

The surface term must be provided by the actual function.

Parameters

so	: input field.
bound	: the surface on which the integral is performed.

Returns: result.

Reimplemented in Kadath::Domain_shell_inner_homothetic, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 187 of file domain.cpp.

References Kadath::Val_domain::check_if_zero(), Kadath::Term_eq::der_t, Kadath::Term_eq::dom, Kadath::Tensor::get_n_comp(), Kadath::Tensor::indices(), Kadath::Domain::integ(), Kadath::Domain::num_dom, Kadath::Term_eq::type_data, and Kadath::Term_eq::val_t.

◆ integ_volume()

double Kadath::Domain_shell::integ_volume ( const Val_domain & so ) const

virtual

Volume integral.

The volume element is provided by the function.

Parameters

so	: the input scalar field.

Returns: the integral.

Reimplemented from Kadath::Domain.

Definition at line 281 of file domain_shell_ope.cpp.

References alpha, Kadath::Base_spectral::bases_1d, Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_base(), Kadath::Val_domain::get_coef(), mult_r(), mult_sin_theta(), Kadath::Domain::nbr_coefs, Kadath::Array< T >::set(), and Kadath::Index::set().

◆ integ_volume_term_eq()

Term_eq Kadath::Domain::integ_volume_term_eq ( const Term_eq & so ) const

virtualinherited

Volume integral of a Term_eq.

The volume term must be provided by the actual function.

Parameters

so	: input field.

Returns: result.

Reimplemented in Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 901 of file domain.cpp.

References Kadath::Val_domain::check_if_zero(), Kadath::Term_eq::der_t, Kadath::Term_eq::get_dom(), Kadath::Val_domain::get_domain(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::indices(), Kadath::Domain::integ_volume(), Kadath::Term_eq::type_data, and Kadath::Term_eq::val_t.

◆ integrale()

double Kadath::Domain::integrale ( const Val_domain & so ) const

virtualinherited

Volume integral.

The volume element is provided by the function (need some cleaning : same as integ_volume)

Parameters

so	: the input scalar field.

Returns: the integral.

Reimplemented in Kadath::Domain_polar_compact, Kadath::Domain_polar_shell, Kadath::Domain_polar_nucleus, Kadath::Domain_oned_inf, Kadath::Domain_oned_qcq, and Kadath::Domain_oned_ori.

Definition at line 1492 of file domain.cpp.

◆ is_in()

bool Kadath::Domain_shell::is_in	(	const Point &	xx,
		double	prec = `1e-13`
	)		const

virtual

Check whether a point lies inside Domain.

Parameters

xx	[input] : the point.
prec	[input] : precision of the computation (used when comparing doubles).

Returns: a true if the point is in the domain and false otherwise.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 169 of file domain_shell.cpp.

References alpha, beta, center, and Kadath::Point::get_ndim().

◆ lap2_term_eq()

Term_eq Kadath::Domain::lap2_term_eq	(	const Term_eq &	so,
		int	m
	)		const

virtualinherited

Returns the flat 2d-Laplacian of Term_eq, for a given harmonic.

Parameters

so	: input field.
m	: the index of the harmonic.

Returns: the 2d-Laplacian.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, and Kadath::Domain_polar_shell_inner_adapted.

Definition at line 161 of file domain.cpp.

References Kadath::Domain::do_comp_by_comp_with_int(), and Kadath::Domain::laplacian2().

◆ lap_term_eq()

Term_eq Kadath::Domain::lap_term_eq	(	const Term_eq &	so,
		int	m
	)		const

virtualinherited

Returns the flat Laplacian of Term_eq, for a given harmonic.

Parameters

so	: input field.
m	: the index of the harmonic.

Returns: the Laplacian.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 157 of file domain.cpp.

References Kadath::Domain::do_comp_by_comp_with_int(), and Kadath::Domain::laplacian().

◆ laplacian()

Val_domain Kadath::Domain::laplacian	(	const Val_domain &	so,
		int	m
	)		const

virtualinherited

Computes the ordinary flat Laplacian for a scalar field with an harmonic index m.

Parameters

so	[input] : the input scalar field.
m	[input] : harmonic index.

Returns: the Laplacian.

Reimplemented in Kadath::Domain_spheric_time_compact, Kadath::Domain_spheric_time_shell, Kadath::Domain_spheric_time_nucleus, Kadath::Domain_spheric_periodic_compact, Kadath::Domain_spheric_periodic_shell, Kadath::Domain_spheric_periodic_nucleus, Kadath::Domain_polar_compact, Kadath::Domain_polar_shell, Kadath::Domain_polar_nucleus, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 87 of file domain.cpp.

References Kadath::Val_domain::der_abs(), and Kadath::Domain::get_ndim().

◆ laplacian2()

Val_domain Kadath::Domain_shell::laplacian2	(	const Val_domain &	so,
		int	m
	)		const

virtual

Computes the ordinary flat 2dè- Laplacian for a scalar field with an harmonic index m.

Parameters

so	[input] : the input scalar field.
m	[input] : harmonic index.

Returns: the 2d-Laplacian.

Reimplemented from Kadath::Domain.

Definition at line 271 of file domain_shell_ope.cpp.

References alpha, Kadath::Val_domain::der_var(), div_r(), and Kadath::Val_domain::div_sin_theta().

◆ mult()

Base_spectral Kadath::Domain_shell::mult	(	const Base_spectral &	,
		const Base_spectral &
	)		const

virtual

Method for the multiplication of two Base_spectral.

Returns: the output base is undefined if the result is not implemented (i.e. if one tries to multiply cosines with Chebyshev polynomials for instance).

Reimplemented from Kadath::Domain.

Definition at line 725 of file domain_shell.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Index::inc(), and Kadath::Base_spectral::ndim.

◆ mult_1mrsL()

Val_domain Kadath::Domain_shell::mult_1mrsL ( const Val_domain & so ) const

virtual

Multiplication by .

Parameters

so	: the input

Returns: the output

Reimplemented from Kadath::Domain.

Definition at line 167 of file domain_shell_ope.cpp.

References alpha, Kadath::Val_domain::base, beta, Kadath::Val_domain::check_if_zero(), and Kadath::Domain::get_radius().

◆ mult_cos_phi()

Val_domain Kadath::Domain_shell::mult_cos_phi ( const Val_domain & ) const

virtual

Multiplication by $\cos \varphi$ .

Reimplemented from Kadath::Domain.

Definition at line 36 of file domain_shell_ope.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Val_domain::base, Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Base_spectral::def, Kadath::Val_domain::in_coef, Kadath::Index::inc(), Kadath::Domain::nbr_coefs, and Kadath::Base_spectral::ope_1d().

◆ mult_cos_theta()

Val_domain Kadath::Domain_shell::mult_cos_theta ( const Val_domain & ) const

virtual

Multiplication by $\cos \theta$ .

Reimplemented from Kadath::Domain.

Definition at line 112 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ mult_cos_time()

Val_domain Kadath::Domain::mult_cos_time ( const Val_domain & ) const

virtualinherited

Multiplication by $\cos \omega t$ .

Reimplemented in Kadath::Domain_polar_periodic_shell, and Kadath::Domain_polar_periodic_nucleus.

Definition at line 1315 of file domain.cpp.

◆ mult_r()

Val_domain Kadath::Domain_shell::mult_r ( const Val_domain & so ) const

virtual

Multiplication by .

Parameters

so	: the input

Returns: the output

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 156 of file domain_shell_ope.cpp.

References alpha, Kadath::Val_domain::base, beta, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ mult_r_term_eq()

Term_eq Kadath::Domain::mult_r_term_eq ( const Term_eq & so ) const

virtualinherited

Multiplication by $r$ of a Term_eq.

Parameters

so	: input field.

Returns: result.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 165 of file domain.cpp.

References Kadath::Domain::do_comp_by_comp(), and Kadath::Domain::mult_r().

◆ mult_sin_phi()

Val_domain Kadath::Domain_shell::mult_sin_phi ( const Val_domain & ) const

virtual

Multiplication by $\sin \varphi$ .

Reimplemented from Kadath::Domain.

Definition at line 74 of file domain_shell_ope.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Val_domain::base, Kadath::Base_spectral::bases_1d, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Base_spectral::def, Kadath::Val_domain::in_coef, Kadath::Index::inc(), Kadath::Domain::nbr_coefs, and Kadath::Base_spectral::ope_1d().

◆ mult_sin_theta()

Val_domain Kadath::Domain_shell::mult_sin_theta ( const Val_domain & ) const

virtual

Multiplication by $\sin \theta$ .

Reimplemented from Kadath::Domain.

Definition at line 123 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ mult_sin_time()

Val_domain Kadath::Domain::mult_sin_time ( const Val_domain & ) const

virtualinherited

Multiplication by $\sin \omega t$ .

Reimplemented in Kadath::Domain_polar_periodic_shell, and Kadath::Domain_polar_periodic_nucleus.

Definition at line 1321 of file domain.cpp.

◆ mult_x()

Val_domain Kadath::Domain::mult_x ( const Val_domain & so ) const

virtualinherited

Multiplication by .

Parameters

so	: the input

Returns: the output

Reimplemented in Kadath::Domain_oned_inf.

Definition at line 1309 of file domain.cpp.

◆ mult_xm1()

Val_domain Kadath::Domain_shell::mult_xm1 ( const Val_domain & ) const

virtual

Multiplication by .

Reimplemented from Kadath::Domain.

Definition at line 226 of file domain_shell_ope.cpp.

References Kadath::Val_domain::base, Kadath::Val_domain::cf, Kadath::Val_domain::coef(), Kadath::Val_domain::in_coef, and Kadath::Base_spectral::ope_1d().

◆ multipoles_asym() [1/2]

Term_eq Kadath::Domain_shell::multipoles_asym	(	int	k,
		int	j,
		int	bound,
		const Term_eq &	so,
		const Array< double > &	passage
	)		const

virtual

Extraction of a given multipole, at some boundary, for an anti-symmetric scalar function.

Parameters

k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
bound	[input] : the boundary at which the computation is done.
so	[input] : input scalar field.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the multipolar coefficient.

Reimplemented from Kadath::Domain.

Definition at line 402 of file multipoles.cpp.

References Kadath::Val_domain::allocate_conf(), Kadath::Val_domain::c, Kadath::Term_eq::der_t, Kadath::Array< T >::dimensions, Kadath::Domain::get_coloc(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Val_domain::set(), Kadath::Index::set(), Kadath::Val_domain::set_base(), Kadath::Scalar::set_domain(), Kadath::Val_domain::set_zero(), Kadath::Term_eq::type_data, val_boundary(), and Kadath::Term_eq::val_t.

◆ multipoles_asym() [2/2]

double Kadath::Domain_shell::multipoles_asym	(	int	k,
		int	j,
		int	bound,
		const Val_domain &	so,
		const Array< double > &	passage
	)		const

virtual

Extraction of a given multipole, at some boundary, for a anti-symmetric scalar function.

Parameters

k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
bound	[input] : the boundary at which the computation is done.
so	[input] : input scalar field.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the multipolar coefficient.

Reimplemented from Kadath::Domain.

Definition at line 76 of file multipoles_valdomain.cpp.

References Kadath::Array< T >::dimensions, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and val_boundary().

◆ multipoles_sym() [1/2]

Term_eq Kadath::Domain_shell::multipoles_sym	(	int	k,
		int	j,
		int	bound,
		const Term_eq &	so,
		const Array< double > &	passage
	)		const

virtual

Extraction of a given multipole, at some boundary, for a symmetric scalar function.

Parameters

k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
bound	[input] : the boundary at which the computation is done.
so	[input] : input scalar field.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the multipolar coefficient.

Reimplemented from Kadath::Domain.

Definition at line 291 of file multipoles.cpp.

References Kadath::Val_domain::allocate_conf(), Kadath::Val_domain::c, Kadath::Term_eq::der_t, Kadath::Array< T >::dimensions, Kadath::Domain::get_coloc(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Val_domain::set(), Kadath::Index::set(), Kadath::Val_domain::set_base(), Kadath::Scalar::set_domain(), Kadath::Val_domain::set_zero(), Kadath::Term_eq::type_data, val_boundary(), and Kadath::Term_eq::val_t.

◆ multipoles_sym() [2/2]

double Kadath::Domain_shell::multipoles_sym	(	int	k,
		int	j,
		int	bound,
		const Val_domain &	so,
		const Array< double > &	passage
	)		const

virtual

Extraction of a given multipole, at some boundary, for a symmetric scalar function.

Parameters

k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
bound	[input] : the boundary at which the computation is done.
so	[input] : input scalar field.
passage	[input] : passage matrix describing the spherical harmonics.

Returns: the multipolar coefficient.

Reimplemented from Kadath::Domain.

Definition at line 38 of file multipoles_valdomain.cpp.

References Kadath::Array< T >::dimensions, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and val_boundary().

◆ nbr_conditions()

Array< int > Kadath::Domain_shell::nbr_conditions	(	const Tensor &	eq,
		int	dom,
		int	order,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtual

Computes number of discretized equations associated with a given tensorial equation in the bulk.

It takes into account the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
order	: describes the order of the equation (2 for a Laplacian for instance).
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Returns: the number of true conditions, component by component.

Reimplemented from Kadath::Domain.

Definition at line 118 of file domain_shell_nbr_conditions.cpp.

References Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Param_tensor::get_m_order(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_m_order_affected(), Kadath::Tensor::is_m_quant_affected(), nbr_conditions_val_domain(), nbr_conditions_val_domain_mquant(), and Kadath::Array< T >::set().

◆ nbr_conditions_array()

Array< int > Kadath::Domain::nbr_conditions_array	(	const Tensor &	eq,
		int	dom,
		const Array< int > &	order,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtualinherited

Computes number of discretized equations associated with a given tensorial equation in the bulk.

It takes into account the various Galerkin basis used.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
order	: describes the order of the equation, with respect to each variable.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Returns: the number of true conditions, component by component.

Reimplemented in Kadath::Domain_spheric_time_compact, Kadath::Domain_spheric_time_shell, and Kadath::Domain_spheric_time_nucleus.

Definition at line 1510 of file domain.cpp.

◆ nbr_conditions_boundary()

Array< int > Kadath::Domain_shell::nbr_conditions_boundary	(	const Tensor &	eq,
		int	dom,
		int	bound,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtual

Computes number of discretized equations associated with a given tensorial equation on a boundary.

It takes into account the various Galerkin basis used. It is used for implementing boundary conditions and matching ones.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
bound	: the boundary at which the equation is enforced.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Returns: the number of true conditions, component by component.

Reimplemented from Kadath::Domain.

Definition at line 103 of file domain_shell_nbr_conditions_boundary.cpp.

References Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Param_tensor::get_m_order(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_m_order_affected(), Kadath::Tensor::is_m_quant_affected(), nbr_conditions_val_domain_boundary(), nbr_conditions_val_domain_boundary_mquant(), and Kadath::Array< T >::set().

◆ nbr_conditions_boundary_array()

Array< int > Kadath::Domain::nbr_conditions_boundary_array	(	const Tensor &	eq,
		int	dom,
		int	bound,
		const Array< int > &	order,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtualinherited

Computes number of discretized equations associated with a given tensorial equation on a boundary.

It takes into account the various Galerkin basis used. It is used for implementing boundary conditions and matching ones.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
bound	: the boundary at which the equation is enforced.
order	: describes the order of the equation, with respect to each variable. The one normal to the surface is irrelevant.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Returns: the number of true conditions, component by component.

Reimplemented in Kadath::Domain_spheric_time_compact, Kadath::Domain_spheric_time_shell, and Kadath::Domain_spheric_time_nucleus.

Definition at line 1522 of file domain.cpp.

◆ nbr_conditions_boundary_one_side()

Array< int > Kadath::Domain::nbr_conditions_boundary_one_side	(	const Tensor &	eq,
		int	dom,
		int	bound,
		int	n_cmp = `-1`,
		Array< int > **	p_cmp = `0x0`
	)		const

virtualinherited

Computes number of discretized equations associated with a given tensorial equation on a boundary.

The boundary is assumed to also have boundaries. (Used for bispherical coordinates). It takes into account the various Galerkin basis used. It is used for implementing boundary conditions and matching ones.

Parameters

eq	: the residual of the equation.
dom	: the domain considered (should be the same as num_dom).
bound	: the boundary at which the equation is enforced.
n_cmp	: number of components of `eq` to be considered. All the components are used of it is -1.
p_cmp	: pointer on the indexes of the components to be considered. Not used of n_cmp = -1 .

Returns: the number of true conditions, component by component.

Reimplemented in Kadath::Domain_bispheric_eta_first, Kadath::Domain_bispheric_chi_first, and Kadath::Domain_bispheric_rect.

Definition at line 1527 of file domain.cpp.

◆ nbr_conditions_val_domain()

int Kadath::Domain_shell::nbr_conditions_val_domain	(	const Val_domain &	so,
		int	mlim,
		int	order
	)		const

Computes number of discretized equations associated with a given tensorial equation in the bulk.

It takes into account the various Galerkin basis used.

Parameters

so	: the residual of the equation.
mlim	: limit for the regularity.
order	: order of the equation (i.e. 2 for a Laplacian for instance)

Returns: the number of true unknowns.

Definition at line 72 of file domain_shell_nbr_conditions.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::get_base(), Kadath::Index::inc(), and Kadath::Domain::nbr_coefs.

◆ nbr_conditions_val_domain_boundary()

int Kadath::Domain_shell::nbr_conditions_val_domain_boundary	(	const Val_domain &	so,
		int	mlim
	)		const

Computes number of discretized equations associated with a given equation on a boundary.

It takes into account the various Galerkin basis used. It is used for implementing boundary conditions and matching ones.

Parameters

so	: the residual of the equation.
mlim	: limit for the regularity.

Returns: the number of true conditions.

Definition at line 62 of file domain_shell_nbr_conditions_boundary.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::get_base(), and Kadath::Domain::nbr_coefs.

◆ nbr_conditions_val_domain_boundary_mquant()

int Kadath::Domain_shell::nbr_conditions_val_domain_boundary_mquant	(	const Val_domain &	so,
		int	mquant
	)		const

Computes number of discretized equations associated with a given equation on a boundary.

It takes into account the various Galerkin basis used. It is used for implementing boundary conditions and matching ones.

Parameters

so	: the residual of the equation.
mquant	: quantum number wrt $\varphi$ .

Returns: the number of true conditions.

Definition at line 27 of file domain_shell_nbr_conditions_boundary.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::get_base(), and Kadath::Domain::nbr_coefs.

◆ nbr_conditions_val_domain_mquant()

int Kadath::Domain_shell::nbr_conditions_val_domain_mquant	(	const Val_domain &	so,
		int	mquant,
		int	order
	)		const

Computes number of discretized equations associated with a given tensorial equation in the bulk.

It takes into account the various Galerkin basis used.

Parameters

so	: the residual of the equation.
mquant	: quantum number wrt $\varphi$ .
order	: order of the equation (i.e. 2 for a Laplacian for instance)

Returns: the number of true unknowns.

Definition at line 29 of file domain_shell_nbr_conditions.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::get_base(), Kadath::Index::inc(), and Kadath::Domain::nbr_coefs.

◆ nbr_points_boundary()

int Kadath::Domain_shell::nbr_points_boundary	(	int	bound,
		const Base_spectral &	base
	)		const

virtual

Computes the number of relevant collocation points on a boundary.

Parameters

bound	: the boundary.
base	: the spectral basis. Its symmetries are used to get the right result.

Returns: the true number of degrees of freedom on the boundary.

Reimplemented from Kadath::Domain.

Definition at line 76 of file domain_shell_systems.cpp.

References Kadath::Base_spectral::bases_1d, and Kadath::Domain::nbr_points.

◆ nbr_unknowns()

int Kadath::Domain_shell::nbr_unknowns	(	const Tensor &	so,
		int	dom
	)		const

virtual

Computes the number of true unknowns of a Tensor, in a given domain.

It takes into account the various symmetries and regularity conditions to determine the precise number of degrees of freedom.

Parameters

so	: the tensorial field.
dom	: the domain considered (should be the same as num_dom).

Returns: the number of true unknowns.

Reimplemented from Kadath::Domain.

Definition at line 108 of file domain_shell_nbr_unknowns.cpp.

References Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Space::get_domain(), Kadath::Param_tensor::get_m_quant(), Kadath::Tensor::get_n_comp(), Kadath::Tensor::get_parameters(), Kadath::Tensor::get_space(), Kadath::Tensor::get_valence(), Kadath::Tensor::is_m_quant_affected(), nbr_unknowns_val_domain(), and nbr_unknowns_val_domain_mquant().

◆ nbr_unknowns_from_adapted()

virtual int Kadath::Domain::nbr_unknowns_from_adapted ( ) const

inlinevirtualinherited

Gives the number of unknowns coming from the variable shape of the domain.

Reimplemented in Kadath::Domain_shell_outer_homothetic, Kadath::Domain_shell_inner_homothetic, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 895 of file space.hpp.

◆ nbr_unknowns_val_domain()

int Kadath::Domain_shell::nbr_unknowns_val_domain	(	const Val_domain &	so,
		int	mlim
	)		const

Computes the number of true unknowns of a Val_domain.

It takes into account the various symmetries and regularity conditions to determine the precise number of degrees of freedom.

Parameters

so	: the field.
mlim	limit for the regularity.

Returns: the number of true unknowns.

Definition at line 66 of file domain_shell_nbr_unknowns.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::get_base(), Kadath::Index::inc(), and Kadath::Domain::nbr_coefs.

◆ nbr_unknowns_val_domain_mquant()

int Kadath::Domain_shell::nbr_unknowns_val_domain_mquant	(	const Val_domain &	so,
		int	mquant
	)		const

Computes the number of true unknowns of a Val_domain.

It takes into account the various symmetries and regularity conditions to determine the precise number of degrees of freedom.

Parameters

so	: the field.
mquant	quantum number wrt $\varphi$ .

Returns: the number of true unknowns.

Definition at line 28 of file domain_shell_nbr_unknowns.cpp.

References Kadath::Base_spectral::bases_1d, Kadath::Val_domain::get_base(), Kadath::Index::inc(), and Kadath::Domain::nbr_coefs.

◆ partial_cart()

Term_eq Kadath::Domain::partial_cart ( const Term_eq & so ) const

virtualinherited

Computes the part of the gradient containing the partial derivative of the field, in Cartesian coordinates.

Parameters

so	: the input `Term_eq`

Returns: the result.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 338 of file domain.cpp.

References Kadath::Term_eq::der_t, Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_space(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Base_tensor::set_basis(), Kadath::Scalar::set_domain(), and Kadath::Term_eq::val_t.

◆ partial_mtz()

Term_eq Kadath::Domain::partial_mtz ( const Term_eq & so ) const

virtualinherited

Computes the part of the gradient containing the partial derivative of the field, in orthonormal coordinates where the constant radius sections have negative curvature.

Parameters

so	: the input `Term_eq`

Returns: the result, being $(\partial_r, \frac{\cos \theta}{r} \partial_\theta , \frac{\cos \theta}{r \sin \theta} \partial_\varphi)$

Definition at line 463 of file domain.cpp.

References Kadath::Domain::der_r(), Kadath::Term_eq::der_t, Kadath::Val_domain::div_r(), Kadath::Val_domain::div_sin_theta(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_space(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Val_domain::mult_cos_theta(), Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Base_tensor::set_basis(), Kadath::Scalar::set_domain(), and Kadath::Term_eq::val_t.

◆ partial_spher()

Term_eq Kadath::Domain::partial_spher ( const Term_eq & so ) const

virtualinherited

Computes the part of the gradient containing the partial derivative of the field, in spherical orthonormal coordinates.

Parameters

so	: the input `Term_eq`

Returns: the result, being $(\partial_r, \partial_\theta /r , \partial_\varphi/r/sin\theta)$

Reimplemented in Kadath::Domain_polar_periodic_shell, Kadath::Domain_polar_periodic_nucleus, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 383 of file domain.cpp.

References Kadath::Domain::der_r(), Kadath::Term_eq::der_t, Kadath::Val_domain::div_r(), Kadath::Val_domain::div_sin_theta(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_space(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Base_tensor::set_basis(), Kadath::Scalar::set_domain(), and Kadath::Term_eq::val_t.

◆ print()

ostream & Kadath::Domain_shell::print ( ostream & o ) const

virtual

Delegate function to virtualize the << operator.

Parameters

o	reference toward the output stream.

Returns: the reference toward output stream that was passed as argument.

Implements Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 63 of file domain_shell.cpp.

References alpha, beta, center, and Kadath::Domain::nbr_points.

◆ radial_part_asym()

Term_eq Kadath::Domain_shell::radial_part_asym	(	const Space &	space,
		int	k,
		int	j,
		const Term_eq &	omega,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &)	f,
		const Param &	param
	)		const

virtual

Gives some radial fit for a given multipole, intended for anti-symmetric scalar function.

Parameters

space	[input] : the concerned `Space`.
k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
omega	[input] : angular velocity.
f	[input] : pointer on the radial function describing the fit.
param	[input] : parameters of the radial fit.

Returns: the radial fit.

Reimplemented from Kadath::Domain.

Definition at line 524 of file multipoles.cpp.

References Kadath::Term_eq::type_data.

◆ radial_part_sym()

Term_eq Kadath::Domain_shell::radial_part_sym	(	const Space &	space,
		int	k,
		int	j,
		const Term_eq &	omega,
		Term_eq(*)(const Space &, int, int, const Term_eq &, const Param &)	f,
		const Param &	param
	)		const

virtual

Gives some radial fit for a given multipole, intended for symmetric scalar function.

Parameters

space	[input] : the concerned `Space`.
k	[input] : index of the spherical harmonic for $\varphi$ .
j	[input] : index of the spherical harmonic for $\theta$ .
omega	[input] : angular velocity.
f	[input] : pointer on the radial function describing the fit.
param	[input] : parameters of the radial fit.

Returns: the radial fit.

Reimplemented from Kadath::Domain.

Definition at line 510 of file multipoles.cpp.

References Kadath::Term_eq::type_data.

◆ save()

void Kadath::Domain_shell::save ( FILE * fd ) const

virtual

Saving function.

Reimplemented from Kadath::Domain.

Reimplemented in Kadath::Domain_shell_surr, and Kadath::Domain_shell_log.

Definition at line 53 of file domain_shell.cpp.

References alpha, beta, center, Kadath::Domain::nbr_coefs, Kadath::Domain::nbr_points, Kadath::Domain::ndim, Kadath::Dim_array::save(), Kadath::Point::save(), and Kadath::Domain::type_base.

◆ set_anti_cheb_base()

void Kadath::Domain_shell::set_anti_cheb_base ( Base_spectral & so ) const

privatevirtual

Sets the base to the standard one for Chebyshev polynomials for functions antisymetric in $ z=0 $ The bases are :

$cos(m\varphi^\star)$ and $sin(m\varphi^\star)$ .
$cos((2j+1)\theta^\star)$ for even ( ) and $sin((2j) \theta^\star)$ for odd ( ).
$T_{i} (x)$ .

If type_coloc changes, coloc is uupdated and the derivative members destroyed.

Parameters

so	[output] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 360 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_anti_cheb_base_with_m()

void Kadath::Domain::set_anti_cheb_base_with_m	(	Base_spectral &	so,
		int	m
	)		const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for functions antisymetric with respect to .

Used for a spherical harmonic .

Parameters

so	[input] : the returned base.
m	[input] : index of the spherical harmonic.

Reimplemented in Kadath::Domain_polar_periodic_shell, Kadath::Domain_polar_periodic_nucleus, Kadath::Domain_polar_compact, Kadath::Domain_polar_shell, Kadath::Domain_polar_nucleus, Kadath::Domain_polar_shell_outer_adapted, and Kadath::Domain_polar_shell_inner_adapted.

Definition at line 1024 of file domain.cpp.

◆ set_anti_legendre_base()

void Kadath::Domain_shell::set_anti_legendre_base ( Base_spectral & so ) const

privatevirtual

Sets the base to the standard one for Legendre polynomials for functions antisymetric in $ z=0 $ The bases are :

$cos(m\varphi^\star)$ and $sin(m\varphi^\star)$ .
$cos((2j+1)\theta^\star)$ for even ( ) and $sin((2j) \theta^\star)$ for odd ( ).
$T_{i} (x)$ .

If type_coloc changes, coloc is uupdated and the derivative members destroyed.

Parameters

so	[output] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 544 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_anti_legendre_base_with_m()

void Kadath::Domain::set_anti_legendre_base_with_m	(	Base_spectral &	so,
		int	m
	)		const

privatevirtualinherited

Gives the base using Legendre polynomials, for functions antisymetric with respect to .

Used for a spherical harmonic .

Parameters

so	[input] : the returned base.
m	[input] : index of the spherical harmonic.

Reimplemented in Kadath::Domain_polar_periodic_shell, Kadath::Domain_polar_periodic_nucleus, Kadath::Domain_polar_compact, Kadath::Domain_polar_shell, Kadath::Domain_polar_nucleus, Kadath::Domain_polar_shell_outer_adapted, and Kadath::Domain_polar_shell_inner_adapted.

Definition at line 1030 of file domain.cpp.

◆ set_cheb_base()

void Kadath::Domain_shell::set_cheb_base ( Base_spectral & so ) const

privatevirtual

Sets the base to the standard one for Chebyshev polynomials.

The bases are :

$cos(m\varphi^\star)$ and $sin(m\varphi^\star)$ .
$cos((2j)\theta^\star)$ for even ( ) and $sin((2j+1) \theta^\star)$ for odd ( ).
$T_{i} (x)$ .

If type_coloc changes, coloc is uupdated and the derivative members destroyed.

Parameters

so	[output] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 288 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_odd()

void Kadath::Domain::set_cheb_base_odd ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using odd Chebyshev polynomials$.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_spheric_periodic_compact, Kadath::Domain_spheric_periodic_shell, Kadath::Domain_spheric_periodic_nucleus, Kadath::Domain_oned_inf, Kadath::Domain_oned_qcq, and Kadath::Domain_oned_ori.

Definition at line 1158 of file domain.cpp.

◆ set_cheb_base_p_mtz()

void Kadath::Domain_shell::set_cheb_base_p_mtz ( Base_spectral & so ) const

privatevirtual

Gives the base using Chebyshev polynomials, for the $\varphi$ component of a vector in the MTZ setting.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 497 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_p_spher()

void Kadath::Domain_shell::set_cheb_base_p_spher ( Base_spectral & so ) const

privatevirtual

Gives the base using Chebyshev polynomials, for the $\varphi$ component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 429 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_r_mtz()

void Kadath::Domain_shell::set_cheb_base_r_mtz ( Base_spectral & so ) const

privatevirtual

Gives the base using Chebyshev polynomials, for the radial component of a vector in the MTZ setting.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 451 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_r_spher()

void Kadath::Domain_shell::set_cheb_base_r_spher ( Base_spectral & so ) const

privatevirtual

Gives the base using Chebyshev polynomials, for the radial component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 383 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_rp_spher()

void Kadath::Domain::set_cheb_base_rp_spher ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the $(r, \varphi)$ component of a 2-tensor.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1112 of file domain.cpp.

◆ set_cheb_base_rt_spher()

void Kadath::Domain::set_cheb_base_rt_spher ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the $(r, \theta)$ component of a 2-tensor.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1106 of file domain.cpp.

◆ set_cheb_base_t_mtz()

void Kadath::Domain_shell::set_cheb_base_t_mtz ( Base_spectral & so ) const

privatevirtual

Gives the base using Chebyshev polynomials, for the $\theta$ component of a vector in the MTZ setting.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 474 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_t_spher()

void Kadath::Domain_shell::set_cheb_base_t_spher ( Base_spectral & so ) const

privatevirtual

Gives the base using Chebyshev polynomials, for the $\theta$ component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 406 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_tp_spher()

void Kadath::Domain::set_cheb_base_tp_spher ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the $(\theta, \varphi)$ component of a 2-tensor.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1118 of file domain.cpp.

◆ set_cheb_base_with_m()

void Kadath::Domain_shell::set_cheb_base_with_m	(	Base_spectral &	so,
		int	m
	)		const

privatevirtual

Gives the standard base using Chebyshev polynomials.

Used for a spherical harmonic .

Parameters

so	[input] : the returned base.
m	[input] : index of the spherical harmonic.

Reimplemented from Kadath::Domain.

Definition at line 311 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_cheb_base_x_cart()

void Kadath::Domain::set_cheb_base_x_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_fourD_periodic_shell, Kadath::Domain_compact_symphi, Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1188 of file domain.cpp.

References Kadath::Domain::set_cheb_base().

◆ set_cheb_base_xy_cart()

void Kadath::Domain::set_cheb_base_xy_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1169 of file domain.cpp.

◆ set_cheb_base_xz_cart()

void Kadath::Domain::set_cheb_base_xz_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1176 of file domain.cpp.

◆ set_cheb_base_y_cart()

void Kadath::Domain::set_cheb_base_y_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_fourD_periodic_shell, Kadath::Domain_compact_symphi, Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1194 of file domain.cpp.

References Kadath::Domain::set_cheb_base().

◆ set_cheb_base_yz_cart()

void Kadath::Domain::set_cheb_base_yz_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1183 of file domain.cpp.

◆ set_cheb_base_z_cart()

void Kadath::Domain::set_cheb_base_z_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_compact_symphi, Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1200 of file domain.cpp.

References Kadath::Domain::set_anti_cheb_base().

◆ set_cheb_r_base()

void Kadath::Domain_shell::set_cheb_r_base ( Base_spectral & so ) const

privatevirtual

Gives the base using odd Chebyshev polynomials$ for the radius.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 351 of file domain_shell.cpp.

References set_cheb_base().

◆ set_cheb_todd_base()

void Kadath::Domain::set_cheb_todd_base ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for odd functions in $ T$ (critic space case)

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_critic_outer, and Kadath::Domain_critic_inner.

Definition at line 1048 of file domain.cpp.

◆ set_cheb_xodd_base()

void Kadath::Domain::set_cheb_xodd_base ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for odd functions in $ X$ (critic space case)

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_critic_inner.

Definition at line 1036 of file domain.cpp.

◆ set_cheb_xodd_todd_base()

void Kadath::Domain::set_cheb_xodd_todd_base ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for odd functions in $ X$ and in $ T$ (critic space case)

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_critic_inner.

Definition at line 1060 of file domain.cpp.

◆ set_legendre_base()

void Kadath::Domain_shell::set_legendre_base ( Base_spectral & so ) const

privatevirtual

Sets the base to the standard one for Legendre polynomials.

The bases are :

$cos(m\varphi^\star)$ and $sin(m\varphi^\star)$ .
$cos((2j)\theta^\star)$ for even ( ) and $sin((2j+1) \theta^\star)$ for odd ( ).
$P_{i} (x)$ .

If type_coloc changes, coloc is uupdated and the derivative members destroyed.

Parameters

so	[output] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 521 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_legendre_base_odd()

void Kadath::Domain::set_legendre_base_odd ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using odd Legendre polynomials$.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_spheric_periodic_compact, Kadath::Domain_spheric_periodic_shell, Kadath::Domain_spheric_periodic_nucleus, Kadath::Domain_oned_inf, Kadath::Domain_oned_qcq, and Kadath::Domain_oned_ori.

Definition at line 1164 of file domain.cpp.

◆ set_legendre_base_p_mtz()

void Kadath::Domain_shell::set_legendre_base_p_mtz ( Base_spectral & so ) const

privatevirtual

Gives the base using Legendre polynomials, for the $\varphi$ component of a vector in the MTZ context.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 681 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_legendre_base_p_spher()

void Kadath::Domain_shell::set_legendre_base_p_spher ( Base_spectral & so ) const

privatevirtual

Gives the base using Legendre polynomials, for the $\varphi$ component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 612 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_legendre_base_r_mtz()

void Kadath::Domain_shell::set_legendre_base_r_mtz ( Base_spectral & so ) const

privatevirtual

Gives the base using Legendre polynomials, for the radial component of a vector in the MTZ context.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 635 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_legendre_base_r_spher()

void Kadath::Domain_shell::set_legendre_base_r_spher ( Base_spectral & so ) const

privatevirtual

Gives the base using Legendre polynomials, for the radial component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 566 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_legendre_base_t_mtz()

void Kadath::Domain_shell::set_legendre_base_t_mtz ( Base_spectral & so ) const

privatevirtual

Gives the base using Legendre polynomials, for the $\theta$ component of a vector in the MTZ context.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 658 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_legendre_base_t_spher()

void Kadath::Domain_shell::set_legendre_base_t_spher ( Base_spectral & so ) const

privatevirtual

Gives the base using Legendre polynomials, for the $\theta$ component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 589 of file domain_shell.cpp.

References Kadath::Base_spectral::allocate(), Kadath::Base_spectral::bases_1d, Kadath::Base_spectral::def, Kadath::Domain::nbr_coefs, Kadath::Index::set(), and Kadath::Domain::type_base.

◆ set_legendre_base_with_m()

void Kadath::Domain::set_legendre_base_with_m	(	Base_spectral &	so,
		int	m
	)		const

privatevirtualinherited

Gives the stnadard base using Legendre polynomials.

Used for a spherical harmonic .

Parameters

so	[input] : the returned base.
m	[input] : index of the spherical harmonic.

Reimplemented in Kadath::Domain_polar_periodic_shell, Kadath::Domain_polar_periodic_nucleus, Kadath::Domain_polar_compact, Kadath::Domain_polar_shell, Kadath::Domain_polar_nucleus, Kadath::Domain_polar_shell_outer_adapted, and Kadath::Domain_polar_shell_inner_adapted.

Definition at line 1018 of file domain.cpp.

◆ set_legendre_base_x_cart()

void Kadath::Domain::set_legendre_base_x_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Legendre polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_fourD_periodic_shell, Kadath::Domain_compact_symphi, Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1206 of file domain.cpp.

References Kadath::Domain::set_legendre_base().

◆ set_legendre_base_y_cart()

void Kadath::Domain::set_legendre_base_y_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Legendre polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_fourD_periodic_shell, Kadath::Domain_compact_symphi, Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1212 of file domain.cpp.

References Kadath::Domain::set_legendre_base().

◆ set_legendre_base_z_cart()

void Kadath::Domain::set_legendre_base_z_cart ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Legendre polynomials, for the component of a vector.

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_compact_symphi, Kadath::Domain_shell_symphi, and Kadath::Domain_nucleus_symphi.

Definition at line 1218 of file domain.cpp.

References Kadath::Domain::set_anti_legendre_base().

◆ set_legendre_r_base()

void Kadath::Domain_shell::set_legendre_r_base ( Base_spectral & so ) const

privatevirtual

Gives the base using odd Legendre polynomials$ for the radius.

Parameters

so	[input] : the returned base.

Reimplemented from Kadath::Domain.

Definition at line 355 of file domain_shell.cpp.

References set_legendre_base().

◆ set_legendre_todd_base()

void Kadath::Domain::set_legendre_todd_base ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Legendre polynomials, for odd functions in $ T$ (critic space case)

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_critic_outer, and Kadath::Domain_critic_inner.

Definition at line 1054 of file domain.cpp.

◆ set_legendre_xodd_base()

void Kadath::Domain::set_legendre_xodd_base ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Legendre polynomials, for odd functions in $ X$ (critic space case)

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_critic_inner.

Definition at line 1042 of file domain.cpp.

◆ set_legendre_xodd_todd_base()

void Kadath::Domain::set_legendre_xodd_todd_base ( Base_spectral & so ) const

privatevirtualinherited

Gives the base using Chebyshev polynomials, for odd functions in $ X$ and in $ T$ (critic space case)

Parameters

so	[input] : the returned base.

Reimplemented in Kadath::Domain_critic_inner.

Definition at line 1066 of file domain.cpp.

◆ set_val_inf()

void Kadath::Domain::set_val_inf	(	Val_domain &	so,
		double	xx
	)		const

virtualinherited

Sets the value at infinity of a Val_domain : not implemented for this type of Domain.

Parameters

so	[input/output] : the `Val_domain`.
xx	[input] : value at infinity.

Reimplemented in Kadath::Domain_compact_symphi, Kadath::Domain_spheric_periodic_compact, Kadath::Domain_polar_compact, Kadath::Domain_oned_inf, and Kadath::Domain_compact.

Definition at line 1266 of file domain.cpp.

◆ srdr()

Val_domain Kadath::Domain::srdr ( const Val_domain & so ) const

virtualinherited

Compute the of a scalar field .

Parameters

so	[input] : the input scalar field.

Returns: the result.

Reimplemented in Kadath::Domain_spheric_time_nucleus, Kadath::Domain_nucleus_symphi, Kadath::Domain_spheric_periodic_nucleus, Kadath::Domain_nucleus, Kadath::Domain_polar_periodic_nucleus, and Kadath::Domain_polar_nucleus.

Definition at line 1333 of file domain.cpp.

◆ update_constante() [1/2]

virtual void Kadath::Domain::update_constante	(	const Val_domain &	shape,
		const Scalar &	oldval,
		Scalar &	newval
	)		const

inlinevirtualinherited

Update the value of a scalar, after the shape of the Domain has been changed by the system.

This is intended for constant field and the new valued is computed using a true spectral summation.

Parameters

shape	: modification to the shape of the `Domain`.
oldval	: old value of the scalar field.
newval	: new value of the scalar field.

Reimplemented in Kadath::Domain_shell_outer_homothetic, Kadath::Domain_shell_inner_homothetic, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 961 of file space.hpp.

◆ update_constante() [2/2]

virtual void Kadath::Domain::update_constante	(	double	bound,
		const Scalar &	oldval,
		Scalar &	newval
	)		const

inlinevirtualinherited

Update the value of a scalar, after the shape of the Domain has been changed by the system.

This is intended for constant field and the new valued is computed using a true spectral summation.

Parameters

bound	: modification to the bound of the `Domain`.
oldval	: old value of the scalar field.
newval	: new value of the scalar field.

Definition at line 970 of file space.hpp.

◆ update_mapping() [1/2]

virtual void Kadath::Domain::update_mapping ( const Val_domain & shape )

inlinevirtualinherited

Updates the variables parts of the Domain.

Parameters

shape : correction to the variable boundary.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 977 of file space.hpp.

◆ update_mapping() [2/2]

virtual void Kadath::Domain::update_mapping ( double bound )

inlinevirtualinherited

Updates the variables parts of the Domain.

Parameters

bound : correction to the variable boundary.

Definition at line 982 of file space.hpp.

◆ update_term_eq()

void Kadath::Domain::update_term_eq ( Term_eq * so ) const

virtualinherited

Update the value of a field, after the shape of the Domain has been changed by the system.

Parameters

so	: pointer on the `Term_eq` to be updated.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 1749 of file domain.cpp.

References Kadath::Term_eq::set_der_zero().

◆ update_variable() [1/2]

virtual void Kadath::Domain::update_variable	(	const Val_domain &	shape,
		const Scalar &	oldval,
		Scalar &	newval
	)		const

inlinevirtualinherited

Update the value of a scalar, after the shape of the Domain has been changed by the system.

This is intended for variable fields and the new valued is computed using a first order Taylor expansion.

Parameters

shape	: modification to the shape of the `Domain`.
oldval	: old value of the scalar field.
newval	: new value of the scalar field.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 942 of file space.hpp.

◆ update_variable() [2/2]

virtual void Kadath::Domain::update_variable	(	double	bound,
		const Scalar &	oldval,
		Scalar &	newval
	)		const

inlinevirtualinherited

Update the value of a scalar, after the shape of the Domain has been changed by the system.

This is intended for variable fields and the new valued is computed using a first order Taylor expansion.

Parameters

bound	: modification of the bound of the `Domain`.
oldval	: old value of the scalar field.
newval	: new value of the scalar field.

Definition at line 952 of file space.hpp.

◆ val_boundary()

double Kadath::Domain_shell::val_boundary	(	int	bound,
		const Val_domain &	so,
		const Index &	ind
	)		const

virtual

Computes the value of a field at a boundary.

The result correspond to one particular coefficient.

Parameters

bound	: name of the boundary at which the result is computed.
so	: input scalar field.
ind	: indexes describing which coefficient is computed. The index corresponding the surface is irrelevant.

Returns: one of the coefficients of the field, on the surface (given by ind).

Reimplemented from Kadath::Domain.

Definition at line 43 of file domain_shell_systems.cpp.

References Kadath::Val_domain::check_if_zero(), Kadath::Val_domain::coef(), Kadath::Val_domain::get_coef(), Kadath::Domain::nbr_coefs, and Kadath::Index::set().

◆ vars_to_terms()

virtual void Kadath::Domain::vars_to_terms ( ) const

inlinevirtualinherited

The Term_eq describing the variable shape of the Domain are updated.

Reimplemented in Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 899 of file space.hpp.

◆ xx_to_ders_from_adapted()

virtual void Kadath::Domain::xx_to_ders_from_adapted	(	const Array< double > &	xx,
		int &	conte
	)		const

inlinevirtualinherited

Affects the derivative part of variable a Domain from a set of values.

Parameters

xx	: set of values used by the affectation
conte	: current position in the values vector.

Reimplemented in Kadath::Domain_shell_outer_homothetic, Kadath::Domain_shell_inner_homothetic, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 928 of file space.hpp.

◆ xx_to_vars_from_adapted() [1/2]

virtual void Kadath::Domain::xx_to_vars_from_adapted	(	double	bound,
		const Array< double > &	xx,
		int &	conte
	)		const

inlinevirtualinherited

Computes the new boundary of a Domain from a set of values.

Parameters

bound	: Variable boundary of the `Domain`.
xx	: set of values used by the affectation
conte	: current position in the values vector.

Definition at line 921 of file space.hpp.

◆ xx_to_vars_from_adapted() [2/2]

virtual void Kadath::Domain::xx_to_vars_from_adapted	(	Val_domain &	shape,
		const Array< double > &	xx,
		int &	conte
	)		const

inlinevirtualinherited

Computes the new boundary of a Domain from a set of values.

Parameters

shape	: `Val_domain` describing the variable boundary of the `Domain`.
xx	: set of values used by the affectation
conte	: current position in the values vector.

Reimplemented in Kadath::Domain_shell_outer_homothetic, Kadath::Domain_shell_inner_homothetic, Kadath::Domain_polar_shell_outer_adapted, Kadath::Domain_polar_shell_inner_adapted, Kadath::Domain_shell_outer_adapted, and Kadath::Domain_shell_inner_adapted.

Definition at line 913 of file space.hpp.

Member Data Documentation

◆ absol

Memory_mapped_array<Val_domain*> Kadath::Domain::absol

mutableprotectedinherited

Asbolute coordinates (if defined ; usually Cartesian-like)

Definition at line 76 of file space.hpp.

◆ alpha

double Kadath::Domain_shell::alpha

private

Relates the numerical to the physical radii.

Definition at line 558 of file spheric.hpp.

◆ beta

double Kadath::Domain_shell::beta

private

Relates the numerical to the physical radii.

Definition at line 559 of file spheric.hpp.

◆ cart

Memory_mapped_array<Val_domain*> Kadath::Domain::cart

mutableprotectedinherited

Cartesian coordinates.

Definition at line 77 of file space.hpp.

◆ cart_surr

Memory_mapped_array<Val_domain*> Kadath::Domain::cart_surr

mutableprotectedinherited

Cartesian coordinates divided by the radius.

Definition at line 79 of file space.hpp.

◆ center

Point Kadath::Domain_shell::center

private

Absolute coordinates of the center.

Definition at line 560 of file spheric.hpp.

◆ coloc

Memory_mapped_array<Array<double>*> Kadath::Domain::coloc

protectedinherited

Colocation points in each dimension (stored in ndim 1d- arrays)

Definition at line 75 of file space.hpp.

◆ nbr_coefs

Dim_array Kadath::Domain::nbr_coefs

mutableprotectedinherited

Number of coefficients.

Definition at line 66 of file space.hpp.

◆ nbr_points

Dim_array Kadath::Domain::nbr_points

protectedinherited

Number of colocation points.

Definition at line 65 of file space.hpp.

◆ ndim

int Kadath::Domain::ndim

protectedinherited

Number of dimensions.

Definition at line 64 of file space.hpp.

◆ num_dom

int Kadath::Domain::num_dom

protectedinherited

Number of the current domain (used by the Space)

Definition at line 63 of file space.hpp.

◆ radius

Val_domain* Kadath::Domain::radius

mutableprotectedinherited

The generalized radius.

Definition at line 78 of file space.hpp.

◆ type_base

int Kadath::Domain::type_base

protectedinherited

Type of colocation point :

CHEB_TYPE : Gauss-Lobato of Chebyshev polynomials.
LEG_TYPE : Gauss-Lobato of Legendre polynomials.

Definition at line 73 of file space.hpp.

The documentation for this class was generated from the following files:

der_var	[input] : the `ndim` derivatives with respect to the numerical coordinates.
der_abs	[output] : the `ndim` derivatives with respect to the absolute Cartesian coordinates.

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Domain_shell() [1/3]

◆ Domain_shell() [2/3]

◆ Domain_shell() [3/3]

Member Function Documentation

◆ absol_to_num()

◆ absol_to_num_bound()

◆ affecte_coef()

◆ affecte_tau()

◆ affecte_tau_one_coef()

◆ affecte_tau_one_coef_val_domain()

◆ affecte_tau_one_coef_val_domain_mquant()

◆ affecte_tau_val_domain()

◆ affecte_tau_val_domain_mquant()

◆ bc_waves() [1/2]

◆ bc_waves() [2/2]

◆ change_basis_cart_to_spher()

◆ change_basis_spher_to_cart()

◆ connection_mtz()

◆ connection_spher()

◆ ddp()

◆ ddr()

◆ ddt()

◆ ddtime()

◆ ddtime_term_eq()

◆ del_deriv()

◆ der_harmonics_asym()

◆ der_harmonics_sym()

◆ der_multipoles_asym()

◆ der_multipoles_sym()

◆ der_normal()

◆ der_normal_term_eq()

◆ der_p()

◆ der_partial_var()

◆ der_r()

◆ der_r_rtwo()

◆ der_radial_part_asym()

◆ der_radial_part_sym()

◆ der_t()

◆ derive_flat_cart()

◆ derive_flat_mtz()

◆ derive_flat_spher()

◆ div_1mrsL()

◆ div_1mx2()

◆ div_1mx2_term_eq()

◆ div_chi()

◆ div_cos_theta()

◆ div_r()

◆ div_r_term_eq()

◆ div_sin_chi()

◆ div_sin_theta()

◆ div_x()

◆ div_xm1()

◆ div_xp1()

◆ do_absol()

◆ do_cart()

◆ do_cart_surr()

◆ do_coloc()

◆ do_comp_by_comp()

◆ do_comp_by_comp_with_int()

◆ do_der_abs_from_der_var()

◆ do_radius()

◆ do_which_points_boundary()

◆ dr_term_eq()

◆ dt()

◆ dtime()

◆ dtime_term_eq()

◆ export_tau()

◆ export_tau_array()

◆ export_tau_boundary()

◆ export_tau_boundary_array()

◆ export_tau_boundary_exception()

◆ export_tau_boundary_one_side()