The Space_bispheric class fills the space with bispherical coordinates (see the constructor for more details). More...

#include <bispheric.hpp>

Inheritance diagram for Kadath::Space_bispheric:

Public Member Functions
int	get_ndom_minus () const
	Accessor ndom_minus. More...

int	get_ndom_plus () const
	Accessor ndom_plus. More...

int	get_nshells () const
	Accessor nshells. More...

	Space_bispheric (int ttype, double dist, double r1, double r2, double rext, int nr)
	Standard constructor More...

	Space_bispheric (int ttype, double dist, double r1, double r2, int nshells, const Array< double > &rr, int nr)
	Constructor with several outer shells. More...

	Space_bispheric (int ttype, double dist, double r1, double r2, int nshells, const Array< double > &rr, const Array< int > &type_r, int nr)
	Constructor with several outer shells possibly of various types (log or mappings). More...

	Space_bispheric (int ttype, double dist, int nminus, const Array< double > &rminus, int nplus, const Array< double > &rplus, int nshells, const Array< double > &rr, const Array< int > &type_r, int nr, bool withnuc=true)
	Constructor with several outer shells possibly of various types (log or mappings). More...

	Space_bispheric (int ttype, double dist, int nminus, const Array< double > &rminus, const Array< int > &type_r_minus, int nplus, const Array< double > &rplus, const Array< int > &type_r_plus, int nshells, const Array< double > &rr, const Array< int > &type_r, int nr, bool withnuc=true)
	Constructor with several outer shells possibly of various types (log or mappings). More...

	Space_bispheric (int ttype, double dist, double rhor1, double rshell1, double rhor2, double rshell2, double rext, int nr)
	Constructor without nucleus and one shell around each holes ; a compactified outer domain. More...

	Space_bispheric (int ttype, double dist, double rhor1, double rshell1, double rhor2, double rshell2, double rext, Dim_array **resol)
	Constructor without nucleus and one shell around each holes ; a compactified outer domain. More...

	Space_bispheric (int ttype, double dist, double rhor1, double rshell1, double rhor2, double rshell2, int nshells, const Array< double > &rshells, int nr)
	Constructor without nucleus and one shell around each holes ; a compactified outer domain. More...

	Space_bispheric (FILE *, int shell_type=0, bool old=false)
	Constructor from a file. More...

	Space_bispheric (FILE *, int type_minus, int type_plus, int shell_type)
	Constructor from a file where the types of shelles are passed as integers. More...

void	add_bc_sphere_one (System_of_eqs &syst, const char eq, int nused=-1, Array< int > *pused=0x0)
	Sets a boundary condition at the inner radius of the first sphere. More...

void	add_bc_sphere_two (System_of_eqs &syst, const char eq, int nused=-1, Array< int > *pused=0x0)
	Sets a boundary condition at the inner radius of the second sphere. More...

void	add_bc_outer_sphere (System_of_eqs &syst, const char eq, int nused=-1, Array< int > *pused=0x0)
	Sets a boundary condition at the outer sphere of the bispheric coordinates. More...

void	add_bc_outer (System_of_eqs &syst, const char eq, int nused=-1, Array< int > *pused=0x0)
	Sets a boundary condition at the outer boundary. More...

void	add_eq (System_of_eqs &syst, const char eq, int nused=-1, Array< int > *pused=0x0)
	Sets an equation inside every domains (assumed to be second order). More...

void	add_eq_full (System_of_eqs &syst, const char eq, int nused=-1, Array< int > *pused=0x0)
	Sets an equation inside every domains (assumed to be zeroth order). More...

void	add_eq_one_side (System_of_eqs &syst, const char eq, int nused=-1, Array< int > *pused=0x0)
	Sets an equation inside every domains (assumed to be first order). More...

void	add_matching (System_of_eqs &syst, const char *rac, const List_comp &list)
	Sets a matching condition accross all the bispheric domain (intended for a second order equation). More...

void	add_matching (System_of_eqs &syst, const char rac, int nused=-1, Array< int > *pused=0x0)
	Sets a matching condition accross all the bispheric domain (intended for a second order equation). More...

void	add_matching_one_side (System_of_eqs &syst, const char rac, int nused=-1, Array< int > *pused=0x0)
	Sets a matching condition accross all the bispheric domain (intended for a first order equation). More...

void	add_eq (System_of_eqs &syst, const char eq, const char rac, const char rac_der, int nused=-1, Array< int > *pused=0x0)
	Adds a bulk equation and two matching conditions. More...

void	add_eq (System_of_eqs &syst, const char eq, const char rac, const char *rac_der, const List_comp &list)
	Adds a bulk equation and two matching conditions. More...

void	add_eq_no_nucleus (System_of_eqs &syst, const char eq, const char rac, const char rac_der, int nused=-1, Array< int > *pused=0x0)
	Adds a bulk equation and two matching conditions for a space without nucleii. More...

void	add_eq_no_nucleus (System_of_eqs &syst, const char eq, const char rac, const char *rac_der, const List_comp &list)
	Adds a bulk equation and two matching conditions for a space without nucleii. More...

void	add_eq_int_inf (System_of_eqs &syst, const char *eq)
	Adds an equation being a surface integral at infinity. More...

void	add_eq_int_sphere_one (System_of_eqs &syst, const char *eq)
	Adds an equation being a surface integral on the first sphere. More...

void	add_eq_int_sphere_two (System_of_eqs &syst, const char *eq)
	Adds an equation being a surface integral on the second sphere. More...

void	add_eq_zero_mode_inf (System_of_eqs &syst, const char *f, int jtarget, int ktarget)
	Adds an equation saying that one coefficient of a field is zero (at infinity) More...

double	get_a_minus () const
	Returns the location of the center of the first sphere. More...

double	get_a_plus () const
	Returns the location of the center of the second sphere. More...

double	int_sphere_one (const Scalar &so) const
	Computes the surface integral on the first sphere. More...

double	int_sphere_two (const Scalar &so) const
	Computes the surface integral on the second sphere. More...

double	int_inf (const Scalar &so) const
	Computes the surface integral at infinity. More...

virtual	~Space_bispheric ()
	Destructor. More...

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

virtual Array< int >	get_indices_matching_non_std (int, int) const
	Gives the number of the other domains, touching a given boundary. More...

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

int	get_nbr_domains () const
	Returns the number of `Domains`. More...

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

const Domain *	get_domain (int i) const
	returns a pointer on the domain. More...

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

virtual void	affecte_coef_to_variable_domains (int &conte, int cc, Array< int > &doms) 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_ders_variable_domains (const Array< double > &xx, int &conte) const
	Update the vairable domains from a set of values. More...

virtual void	xx_to_vars_variable_domains (System_of_eqs *syst, const Array< double > &xx, int &conte) const
	Update the variables of a system, from the variation of the shape of the domains. More...

Protected Attributes
double	a_minus
	X-absolute coordinate of the center of the first sphere. More...

double	a_plus
	X-absolute coordinate of the center of the second sphere. More...

int	ndom_minus
	Number of spherical domains inside the first sphere. More...

int	ndom_plus
	Number of spherical domains inside the second sphere. More...

int	nshells
	Number of shells outside the bispheric region. More...

int	nbr_domains
	Number od `Domains`. More...

int	ndim
	Number of dimensions (should be the same for all the `Domains`). More...

int	type_base
	Type of basis used (i.e. using either Chebyshev or Legendre polynomials). More...

Domain **	domains
	Pointers on the various `Domains`. More...

Detailed Description

The Space_bispheric class fills the space with bispherical coordinates (see the constructor for more details).

Definition at line 1241 of file bispheric.hpp.

Constructor & Destructor Documentation

◆ Space_bispheric() [1/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		double	r1,
		double	r2,
		double	rext,
		int	nr
	)

Standard constructor

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
r1	[input] : radius of the first sphere.
r2	[input] : radius of the second sphere.
rext	[input] : radius of the outer boundary of the bispherical part.
nr	[input] : number of points in each dimension ( for coordinates of the type $\varphi$ )

The scale $ a $ for the bispherical coordinates is determined such that : $\sqrt{a^2 + r_1^2} + \sqrt{a^2 + r_2^2} = d$

The first sphere is described by $\eta_{\rm minus} = -{\rm asinh}\displaystyle\frac{a}{r_1}$ , centered at $x_1 = a \displaystyle\frac{\cosh \eta_{\rm minus}}{\sinh \eta_{\rm minus}}$ .

The second sphere is described by $\eta_{\rm plus} = {\rm asinh}\displaystyle\frac{a}{r_2}$ , centered at $x_2 = a \displaystyle\frac{\cosh \eta_{\rm plus}}{\sinh \eta_{\rm plus}}$ .

The cutoffs for the bispherical coordinates are $\chi_c = 2 {\rm atan}\displaystyle\frac{a}{R}$ and $\eta_c = \ln (\displaystyle\frac{R}{a} + 1) - \ln (\displaystyle\frac{R}{a} - 1)$

The various domains are then :

One Domain_nucleus, of radius , centered at .
One Domain_nucleus, of radius , centered at .
One Domain_bispheric_chi_first near the first sphere.
One Domain_bispheric_rect near the first sphere.
One Domain_bispheric_eta_first inbetween the two spheres.
One Domain_bispheric_rect near the second sphere.
One Domain_bispheric_chi_first near the second sphere.
One Domain_compact centered on the origin, with inner radius .

Definition at line 42 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Dim_array::set(), Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [2/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		double	r1,
		double	r2,
		int	nshells,
		const Array< double > &	rr,
		int	nr
	)

Constructor with several outer shells.

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
r1	[input] : radius of the first sphere.
r2	[input] : radius of the second sphere.
nshells	[input] : number of outer shells.
rr	[input] : radiii of the outer shells.
nr	[input] : number of points in each dimension ( for coordinates of the type $\varphi$ )

The various domains are then :

One Domain_nucleus, of radius , centered at .
One Domain_nucleus, of radius , centered at .
One Domain_bispheric_chi_first near the first sphere.
One Domain_bispheric_rect near the first sphere.
One Domain_bispheric_eta_first inbetween the two spheres.
One Domain_bispheric_rect near the second sphere.
One Domain_bispheric_chi_first near the second sphere.
nshells Domain_shells outside the bispheric region, centered on the origin.
One Domain_compact centered on the origin.

Definition at line 102 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Dim_array::set(), Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [3/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		double	r1,
		double	r2,
		int	nshells,
		const Array< double > &	rr,
		const Array< int > &	type_r,
		int	nr
	)

Constructor with several outer shells possibly of various types (log or $ 1/r$ mappings).

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
r1	[input] : radius of the first sphere.
r2	[input] : radius of the second sphere.
nshells	[input] : number of outer shells.
rr	[input] : radiii of the outer shells.
type_r	[input] : types of the various outer shells.
nr	[input] : number of points in each dimension ( for coordinates of the type $\varphi$ )

The various domains are then :

One Domain_nucleus, of radius , centered at .
One Domain_nucleus, of radius , centered at .
One Domain_bispheric_chi_first near the first sphere.
One Domain_bispheric_rect near the first sphere.
One Domain_bispheric_eta_first inbetween the two spheres.
One Domain_bispheric_rect near the second sphere.
One Domain_bispheric_chi_first near the second sphere.
nshells shells outside the bispheric region, centered on the origin. They can be Domain_shell, Domain_shell_log or Domain_shell_surr
One Domain_compact centered on the origin.

Definition at line 167 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Dim_array::set(), Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [4/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		int	nminus,
		const Array< double > &	rminus,
		int	nplus,
		const Array< double > &	rplus,
		int	nshells,
		const Array< double > &	rr,
		const Array< int > &	type_r,
		int	nr,
		bool	withnuc = `true`
	)

Constructor with several outer shells possibly of various types (log or $ 1/r$ mappings).

Each hole can be described by several shells.

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
nminus	[input] : number of domains inside the first sphere.
rminus	[input] : radii of the domains inside the first sphere.
nplus	[input] : number of domains inside the second sphere.
rplus	[input] : radii of the domains inside the second sphere.
nshells	[input] : number of outer shells.
rr	[input] : radiii of the outer shells.
type_r	[input] : types of the various outer shells.
nr	[input] : number of points in each dimension
withnuc	[input] : states wheather a nucleus is present or not ( for coordinates of the type $\varphi$ )

The various domains are then :

One Domain_nucleus centered at . (if present)
nminus-1 Domain_shell centered at .
One Domain_nucleus centered at . (if present)
nplus-2 Domain_shell centered at .
One Domain_bispheric_chi_first near the first sphere.
One Domain_bispheric_rect near the first sphere.
One Domain_bispheric_eta_first inbetween the two spheres.
One Domain_bispheric_rect near the second sphere.
One Domain_bispheric_chi_first near the second sphere.
nshells shells outside the bispheric region, centered on the origin They can be Domain_shell, Domain_shell_log or Domain_shell_surr
One Domain_compact centered on the origin.

Definition at line 244 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Dim_array::set(), Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [5/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		int	nminus,
		const Array< double > &	rminus,
		const Array< int > &	type_r_minus,
		int	nplus,
		const Array< double > &	rplus,
		const Array< int > &	type_r_plus,
		int	nshells,
		const Array< double > &	rr,
		const Array< int > &	type_r,
		int	nr,
		bool	withnuc = `true`
	)

Constructor with several outer shells possibly of various types (log or $ 1/r$ mappings).

Each hole can be described by several shells also possibly with various types of mappings

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
nminus	[input] : number of domains inside the first sphere.
rminus	[input] : radii of the domains inside the first sphere.
type_r_minus	[input] : types of the various shells around the first hole.
nplus	[input] : number of domains inside the second sphere.
rplus	[input] : radii of the domains inside the second sphere.
type_r_plus	[input] : types of the various shells around the second hole.
nshells	[input] : number of outer shells.
rr	[input] : radiii of the outer shells.
type_r	[input] : types of the various outer shells.
nr	[input] : number of points in each dimension
withnuc	[input] : states wheather a nucleus is present or not ( for coordinates of the type $\varphi$ )

The various domains are then :

One Domain_nucleus centered at . (if present)
nminus-1 Shells centered at . They can be Domain_shell, Domain_shell_log or Domain_shell_surr
One Domain_nucleus centered at (if present)
nplus-2 Shells centered at . They can be Domain_shell, Domain_shell_log or Domain_shell_surr
One Domain_bispheric_chi_first near the first sphere.
One Domain_bispheric_rect near the first sphere.
One Domain_bispheric_eta_first inbetween the two spheres.
One Domain_bispheric_rect near the second sphere.
One Domain_bispheric_chi_first near the second sphere.
nshells shells outside the bispheric region, centered on the origin. They can be Domain_shell, Domain_shell_log or Domain_shell_surr
One Domain_compact centered on the origin.

Definition at line 351 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Dim_array::set(), Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [6/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		double	rhor1,
		double	rshell1,
		double	rhor2,
		double	rshell2,
		double	rext,
		int	nr
	)

Constructor without nucleus and one shell around each holes ; a compactified outer domain.

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
rhor1	[input] : radius of the first horizon.
rshell1	[input] : radius of the first shell.
rhor2	[input] : radius of the second horizon.
rshell2	[input] : radius of the second shell.
rext	[input] : radius of the bispherical domains.
nr	[input] : number of points in each dimension ( for coordinates of the type $\varphi$ )

Definition at line 490 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Dim_array::set(), Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [7/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		double	rhor1,
		double	rshell1,
		double	rhor2,
		double	rshell2,
		double	rext,
		Dim_array **	resol
	)

Constructor without nucleus and one shell around each holes ; a compactified outer domain.

The resolution of each domain is speceified by hand

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
rhor1	[input] : radius of the first horizon.
rshell1	[input] : radius of the first shell.
rhor2	[input] : radius of the second horizon.
rshell2	[input] : radius of the second shell.
rext	[input] : radius of the bispherical domains.
resol	[input] : resolution in each domains

Definition at line 556 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [8/10]

Kadath::Space_bispheric::Space_bispheric	(	int	ttype,
		double	dist,
		double	rhor1,
		double	rshell1,
		double	rhor2,
		double	rshell2,
		int	nshells,
		const Array< double > &	rshells,
		int	nr
	)

Constructor without nucleus and one shell around each holes ; a compactified outer domain.

Parameters

ttype	[input] : the type of basis.
dist	[input] : distance between the centers of the two spheres.
rhor1	[input] : radius of the first horizon.
rshell1	[input] : radius of the first shell.
rhor2	[input] : radius of the second horizon.
rshell2	[input] : radius of the second shell.
nshells	[input] : number of outer shells.
rshells	[input] : radiii of the outer shells.
nr	[input] : number of points in each dimension ( for coordinates of the type $\varphi$ )

Definition at line 616 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Param::add_double(), Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, Kadath::Dim_array::set(), Kadath::Point::set(), and Kadath::Space::type_base.

◆ Space_bispheric() [9/10]

Kadath::Space_bispheric::Space_bispheric	(	FILE *	fd,
		int	shell_type = `0`,
		bool	old = `false`
	)

Constructor from a file.

Parameters

fd	: the file
shell_type	: type of the outer shells (assumed to be the same for each one).
old	: deprecated for backward compatibility.

Definition at line 685 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, and Kadath::Space::type_base.

◆ Space_bispheric() [10/10]

Kadath::Space_bispheric::Space_bispheric	(	FILE *	fd,
		int	type_minus,
		int	type_plus,
		int	shell_type
	)

Constructor from a file where the types of shelles are passed as integers.

Parameters

fd	: the file
type_minus	: type of the shells around hole 1(assumed to be the same for each one).
type_plus	: type of the shells around hole 2 (assumed to be the same for each one).
shell_type	: type of the outer shells (assumed to be the same for each one).

Definition at line 768 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, and Kadath::Space::type_base.

◆ ~Space_bispheric()

Kadath::Space_bispheric::~Space_bispheric ( )

virtual

Destructor.

Definition at line 874 of file space_bispheric.cpp.

Member Function Documentation

◆ add_bc_outer()

void Kadath::Space_bispheric::add_bc_outer	(	System_of_eqs &	syst,
		const char *	eq,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets a boundary condition at the outer boundary.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 55 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_bc(), and Kadath::Space::nbr_domains.

◆ add_bc_outer_sphere()

void Kadath::Space_bispheric::add_bc_outer_sphere	(	System_of_eqs &	syst,
		const char *	eq,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets a boundary condition at the outer sphere of the bispheric coordinates.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 49 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_bc(), ndom_minus, and ndom_plus.

◆ add_bc_sphere_one()

void Kadath::Space_bispheric::add_bc_sphere_one	(	System_of_eqs &	syst,
		const char *	eq,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets a boundary condition at the inner radius of the first sphere.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 26 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_bc(), ndom_minus, and ndom_plus.

◆ add_bc_sphere_two()

void Kadath::Space_bispheric::add_bc_sphere_two	(	System_of_eqs &	syst,
		const char *	eq,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets a boundary condition at the inner radius of the second sphere.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 38 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_bc(), ndom_minus, and ndom_plus.

◆ add_eq() [1/3]

void Kadath::Space_bispheric::add_eq	(	System_of_eqs &	syst,
		const char *	eq,
		const char *	rac,
		const char *	rac_der,
		const List_comp &	list
	)

Adds a bulk equation and two matching conditions.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the bulk equation.
rac	: the string describing the first matching condition.
rac_der	: the string describing the second matching condition.
list	: list of the components to be considered.

Definition at line 156 of file bispheric_add_eq.cpp.

References add_eq(), Kadath::List_comp::get_ncomp(), and Kadath::List_comp::get_pcomp().

◆ add_eq() [2/3]

void Kadath::Space_bispheric::add_eq	(	System_of_eqs &	syst,
		const char *	eq,
		const char *	rac,
		const char *	rac_der,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Adds a bulk equation and two matching conditions.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the bulk equation.
rac	: the string describing the first matching condition.
rac_der	: the string describing the second matching condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 92 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_inside(), Kadath::System_of_eqs::add_eq_matching(), and Kadath::System_of_eqs::add_eq_matching_import().

◆ add_eq() [3/3]

void Kadath::Space_bispheric::add_eq	(	System_of_eqs &	syst,
		const char *	eq,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets an equation inside every domains (assumed to be second order).

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 59 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_inside(), Kadath::System_of_eqs::get_dom_max(), and Kadath::System_of_eqs::get_dom_min().

◆ add_eq_full()

void Kadath::Space_bispheric::add_eq_full	(	System_of_eqs &	syst,
		const char *	eq,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets an equation inside every domains (assumed to be zeroth order).

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 64 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_full(), Kadath::System_of_eqs::get_dom_max(), and Kadath::System_of_eqs::get_dom_min().

◆ add_eq_int_inf()

void Kadath::Space_bispheric::add_eq_int_inf	(	System_of_eqs &	syst,
		const char *	eq
	)

Adds an equation being a surface integral at infinity.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the equation (should contain something like integ(f)=b)

Definition at line 214 of file bispheric_add_eq.cpp.

References Kadath::Space::domains, Kadath::System_of_eqs::eq_int, Kadath::System_of_eqs::give_ope(), Kadath::System_of_eqs::is_ope_bin(), Kadath::System_of_eqs::nbr_conditions, Kadath::Space::nbr_domains, and Kadath::System_of_eqs::neq_int.

◆ add_eq_int_sphere_one()

void Kadath::Space_bispheric::add_eq_int_sphere_one	(	System_of_eqs &	syst,
		const char *	eq
	)

Adds an equation being a surface integral on the first sphere.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the equation (should contain something like integ(f)=b)

Definition at line 252 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::eq_int, Kadath::System_of_eqs::give_ope(), Kadath::System_of_eqs::is_ope_bin(), Kadath::System_of_eqs::nbr_conditions, ndom_minus, ndom_plus, and Kadath::System_of_eqs::neq_int.

◆ add_eq_int_sphere_two()

void Kadath::Space_bispheric::add_eq_int_sphere_two	(	System_of_eqs &	syst,
		const char *	eq
	)

Adds an equation being a surface integral on the second sphere.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the equation (should contain something like integ(f)=b)

Definition at line 305 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::eq_int, Kadath::System_of_eqs::give_ope(), Kadath::System_of_eqs::is_ope_bin(), Kadath::System_of_eqs::nbr_conditions, ndom_minus, ndom_plus, and Kadath::System_of_eqs::neq_int.

◆ add_eq_no_nucleus() [1/2]

void Kadath::Space_bispheric::add_eq_no_nucleus	(	System_of_eqs &	syst,
		const char *	eq,
		const char *	rac,
		const char *	rac_der,
		const List_comp &	list
	)

Adds a bulk equation and two matching conditions for a space without nucleii.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the bulk equation.
rac	: the string describing the first matching condition.
rac_der	: the string describing the second matching condition.
list	: list of the components to be considered.

Definition at line 211 of file bispheric_add_eq.cpp.

References add_eq(), Kadath::List_comp::get_ncomp(), and Kadath::List_comp::get_pcomp().

◆ add_eq_no_nucleus() [2/2]

void Kadath::Space_bispheric::add_eq_no_nucleus	(	System_of_eqs &	syst,
		const char *	eq,
		const char *	rac,
		const char *	rac_der,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Adds a bulk equation and two matching conditions for a space without nucleii.

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the bulk equation.
rac	: the string describing the first matching condition.
rac_der	: the string describing the second matching condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 160 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_inside(), Kadath::System_of_eqs::add_eq_matching(), and Kadath::System_of_eqs::add_eq_matching_import().

◆ add_eq_one_side()

void Kadath::Space_bispheric::add_eq_one_side	(	System_of_eqs &	syst,
		const char *	eq,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets an equation inside every domains (assumed to be first order).

Parameters

syst	: the `System_of_eqs`.
eq	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 69 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_one_side(), Kadath::System_of_eqs::get_dom_max(), and Kadath::System_of_eqs::get_dom_min().

◆ add_eq_zero_mode_inf()

void Kadath::Space_bispheric::add_eq_zero_mode_inf	(	System_of_eqs &	syst,
		const char *	f,
		int	jtarget,
		int	ktarget
	)

Adds an equation saying that one coefficient of a field is zero (at infinity)

Parameters

syst	: the `System_of_eqs`.
f	: the field
jtarget	: the index $\theta$ of the mode that must vanished.
ktarget	: the index $\varphi$ of the mode that must vanished.

Definition at line 358 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_mode(), Kadath::Space::domains, Kadath::Space::nbr_domains, and Kadath::Index::set().

◆ add_matching() [1/2]

void Kadath::Space_bispheric::add_matching	(	System_of_eqs &	syst,
		const char *	rac,
		const List_comp &	list
	)

Sets a matching condition accross all the bispheric domain (intended for a second order equation).

Parameters

syst	: the `System_of_eqs`.
rac	: the string describing the boundary condition.
list	: list of the components to be considered.

Definition at line 81 of file bispheric_add_eq.cpp.

References Kadath::List_comp::get_ncomp(), and Kadath::List_comp::get_pcomp().

◆ add_matching() [2/2]

void Kadath::Space_bispheric::add_matching	(	System_of_eqs &	syst,
		const char *	rac,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets a matching condition accross all the bispheric domain (intended for a second order equation).

Parameters

syst	: the `System_of_eqs`.
rac	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 74 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_matching(), ndom_minus, and ndom_plus.

◆ add_matching_one_side()

void Kadath::Space_bispheric::add_matching_one_side	(	System_of_eqs &	syst,
		const char *	rac,
		int	nused = `-1`,
		Array< int > **	pused = `0x0`
	)

Sets a matching condition accross all the bispheric domain (intended for a first order equation).

Parameters

syst	: the `System_of_eqs`.
rac	: the string describing the boundary condition.
nused	: number of components of `eq` to be considered. All the components are used of it is -1.
pused	: pointer on the indexes of the components to be considered. Not used of nused = -1 .

Definition at line 85 of file bispheric_add_eq.cpp.

References Kadath::System_of_eqs::add_eq_matching_one_side(), ndom_minus, and ndom_plus.

◆ affecte_coef_to_variable_domains()

virtual void Kadath::Space::affecte_coef_to_variable_domains	(	int &	conte,
		int	cc,
		Array< int > &	doms
	)		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.
doms	: Array containing the index of the variable domains present in this space.

Reimplemented in Kadath::Space_bin_ns, Kadath::Space_bin_bh, Kadath::Space_bbh, Kadath::Space_polar_adapted, Kadath::Space_adapted_bh, and Kadath::Space_spheric_adapted.

Definition at line 1401 of file space.hpp.

◆ get_a_minus()

double Kadath::Space_bispheric::get_a_minus ( ) const

inline

Returns the location of the center of the first sphere.

Definition at line 1644 of file bispheric.hpp.

References a_minus.

◆ get_a_plus()

double Kadath::Space_bispheric::get_a_plus ( ) const

inline

Returns the location of the center of the second sphere.

Definition at line 1648 of file bispheric.hpp.

References a_plus.

◆ get_domain()

const Domain* Kadath::Space::get_domain ( int i ) const

inlineinherited

returns a pointer on the domain.

Parameters

i	[input] : the index of the domain.

Definition at line 1385 of file space.hpp.

References Kadath::Space::domains, and Kadath::Space::nbr_domains.

◆ get_indices_matching_non_std()

Array< int > Kadath::Space_bispheric::get_indices_matching_non_std	(	int	dom,
		int	bound
	)		const

virtual

Gives the number of the other domains, touching a given boundary.

It also gives the name of the boundary, as seen by the other domain.

Parameters

dom	: the domain considered.
bound	: the boundary.

Returns: a 2d-array containing the numbers of the other domains (stored in (0,i)) and the names of the boundary (stored in (1,i)).

Reimplemented from Kadath::Space.

Definition at line 892 of file space_bispheric.cpp.

References ndom_minus, ndom_plus, and Kadath::Array< T >::set().

◆ get_nbr_domains()

int Kadath::Space::get_nbr_domains ( ) const

inlineinherited

Returns the number of Domains.

Definition at line 1375 of file space.hpp.

References Kadath::Space::nbr_domains.

◆ get_ndim()

int Kadath::Space::get_ndim ( ) const

inlineinherited

Returns the number of dimensions.

Definition at line 1373 of file space.hpp.

References Kadath::Space::ndim.

◆ get_ndom_minus()

int Kadath::Space_bispheric::get_ndom_minus ( ) const

inline

Accessor ndom_minus.

Definition at line 1253 of file bispheric.hpp.

References ndom_minus.

◆ get_ndom_plus()

int Kadath::Space_bispheric::get_ndom_plus ( ) const

inline

Accessor ndom_plus.

Definition at line 1257 of file bispheric.hpp.

References ndom_plus.

◆ get_nshells()

int Kadath::Space_bispheric::get_nshells ( ) const

inline

Accessor nshells.

Definition at line 1261 of file bispheric.hpp.

References nshells.

◆ get_type_base()

int Kadath::Space::get_type_base ( ) const

inlineinherited

Returns the type of basis.

Definition at line 1377 of file space.hpp.

References Kadath::Space::type_base.

◆ int_inf()

double Kadath::Space_bispheric::int_inf ( const Scalar & so ) const

Computes the surface integral at infinity.

Parameters

so	: the field to be integrated.

Returns: the surface integral.

Definition at line 1041 of file space_bispheric.cpp.

References Kadath::Space::domains, Kadath::Domain_compact::integ(), and Kadath::Space::nbr_domains.

◆ int_sphere_one()

double Kadath::Space_bispheric::int_sphere_one ( const Scalar & so ) const

Computes the surface integral on the first sphere.

Parameters

so	: the field to be integrated.

Returns: the surface integral.

Definition at line 1052 of file space_bispheric.cpp.

References Kadath::Space::domains, Kadath::Domain::integ(), ndom_minus, and ndom_plus.

◆ int_sphere_two()

double Kadath::Space_bispheric::int_sphere_two ( const Scalar & so ) const

Computes the surface integral on the second sphere.

Parameters

so	: the field to be integrated.

Returns: the surface integral.

Definition at line 1062 of file space_bispheric.cpp.

References Kadath::Space::domains, Kadath::Domain::integ(), ndom_minus, and ndom_plus.

◆ nbr_unknowns_from_variable_domains()

virtual int Kadath::Space::nbr_unknowns_from_variable_domains ( ) const

inlinevirtualinherited

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

Reimplemented in Kadath::Space_bin_ns, Kadath::Space_bin_bh, Kadath::Space_bbh, Kadath::Space_polar_adapted, Kadath::Space_adapted_bh, and Kadath::Space_spheric_adapted.

Definition at line 1394 of file space.hpp.

◆ save()

void Kadath::Space_bispheric::save ( FILE * ) const

virtual

Saving function.

Reimplemented from Kadath::Space.

Definition at line 879 of file space_bispheric.cpp.

References a_minus, a_plus, Kadath::Space::domains, Kadath::Space::nbr_domains, Kadath::Space::ndim, ndom_minus, ndom_plus, nshells, and Kadath::Space::type_base.

◆ xx_to_ders_variable_domains()

virtual void Kadath::Space::xx_to_ders_variable_domains	(	const Array< double > &	xx,
		int &	conte
	)		const

inlinevirtualinherited

Update the vairable domains from a set of values.

Parameters

xx	: set of values used by the affectation
conte	: current position in the values vector.

Reimplemented in Kadath::Space_bin_ns, Kadath::Space_bin_bh, Kadath::Space_bbh, Kadath::Space_polar_adapted, Kadath::Space_adapted_bh, and Kadath::Space_spheric_adapted.

Definition at line 1407 of file space.hpp.

◆ xx_to_vars_variable_domains()

virtual void Kadath::Space::xx_to_vars_variable_domains	(	System_of_eqs *	syst,
		const Array< double > &	xx,
		int &	conte
	)		const

inlinevirtualinherited

Update the variables of a system, from the variation of the shape of the domains.

Parameters

syst	: the `System_of_eqs` considered.
xx	: set of values used by the affectation
conte	: current position in the values vector.

Reimplemented in Kadath::Space_bin_ns, Kadath::Space_bin_bh, Kadath::Space_bbh, Kadath::Space_polar_adapted, Kadath::Space_adapted_bh, and Kadath::Space_spheric_adapted.

Definition at line 1414 of file space.hpp.

Member Data Documentation

◆ a_minus

double Kadath::Space_bispheric::a_minus

protected

X-absolute coordinate of the center of the first sphere.

Definition at line 1243 of file bispheric.hpp.

◆ a_plus

double Kadath::Space_bispheric::a_plus

protected

X-absolute coordinate of the center of the second sphere.

Definition at line 1244 of file bispheric.hpp.

◆ domains

Domain** Kadath::Space::domains

protectedinherited

Pointers on the various Domains.

Definition at line 1368 of file space.hpp.

◆ nbr_domains

int Kadath::Space::nbr_domains

protectedinherited

Number od Domains.

Definition at line 1365 of file space.hpp.

◆ ndim

int Kadath::Space::ndim

protectedinherited

Number of dimensions (should be the same for all the Domains).

Definition at line 1366 of file space.hpp.

◆ ndom_minus

int Kadath::Space_bispheric::ndom_minus

protected

Number of spherical domains inside the first sphere.

Definition at line 1245 of file bispheric.hpp.

◆ ndom_plus

int Kadath::Space_bispheric::ndom_plus

protected

Number of spherical domains inside the second sphere.

Definition at line 1246 of file bispheric.hpp.

◆ nshells

int Kadath::Space_bispheric::nshells

protected

Number of shells outside the bispheric region.

Definition at line 1247 of file bispheric.hpp.

◆ type_base

int Kadath::Space::type_base

protectedinherited

Type of basis used (i.e. using either Chebyshev or Legendre polynomials).

Definition at line 1367 of file space.hpp.

The documentation for this class was generated from the following files:

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Space_bispheric() [1/10]

◆ Space_bispheric() [2/10]

◆ Space_bispheric() [3/10]

◆ Space_bispheric() [4/10]

◆ Space_bispheric() [5/10]

◆ Space_bispheric() [6/10]

◆ Space_bispheric() [7/10]

◆ Space_bispheric() [8/10]

◆ Space_bispheric() [9/10]

◆ Space_bispheric() [10/10]

◆ ~Space_bispheric()

Member Function Documentation

◆ add_bc_outer()

◆ add_bc_outer_sphere()

◆ add_bc_sphere_one()

◆ add_bc_sphere_two()

◆ add_eq() [1/3]

◆ add_eq() [2/3]

◆ add_eq() [3/3]

◆ add_eq_full()

◆ add_eq_int_inf()

◆ add_eq_int_sphere_one()

◆ add_eq_int_sphere_two()

◆ add_eq_no_nucleus() [1/2]

◆ add_eq_no_nucleus() [2/2]

◆ add_eq_one_side()

◆ add_eq_zero_mode_inf()

◆ add_matching() [1/2]

◆ add_matching() [2/2]

◆ add_matching_one_side()

◆ affecte_coef_to_variable_domains()

◆ get_a_minus()

◆ get_a_plus()

◆ get_domain()

◆ get_indices_matching_non_std()

◆ get_nbr_domains()

◆ get_ndim()

◆ get_ndom_minus()

◆ get_ndom_plus()

◆ get_nshells()

◆ get_type_base()

◆ int_inf()

◆ int_sphere_one()

◆ int_sphere_two()

◆ nbr_unknowns_from_variable_domains()

◆ save()

◆ xx_to_ders_variable_domains()

◆ xx_to_vars_variable_domains()

Member Data Documentation

◆ a_minus

◆ a_plus

◆ domains

◆ nbr_domains

◆ ndim

◆ ndom_minus

◆ ndom_plus

◆ nshells

◆ type_base