domain_polar_nucleus.cpp

/*
    Copyright 2017 Philippe Grandclement
 
    This file is part of Kadath.
 
    Kadath is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    Kadath is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with Kadath.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#include "headcpp.hpp"
#include "polar.hpp"
#include "point.hpp"
#include "array_math.hpp"
#include "val_domain.hpp"
 
namespace Kadath{
void coef_1d (int, Array<double>&) ;
void coef_i_1d (int, Array<double>&) ;
int der_1d (int, Array<double>&) ;
 
// Standard constructor
Domain_polar_nucleus::Domain_polar_nucleus (int num, int ttype, double r, const Point& cr, const Dim_array& nbr) :  
        Domain(num, ttype, nbr), alpha(r),center(cr) {
     assert (nbr.get_ndim()==2) ;
     assert (cr.get_ndim()==2) ;
     do_coloc() ;
}
 
// Constructor by copy
Domain_polar_nucleus::Domain_polar_nucleus (const Domain_polar_nucleus& so) : Domain(so), alpha(so.alpha), center(so.center) {
}
 
Domain_polar_nucleus::Domain_polar_nucleus (int num, FILE* fd) : Domain(num, fd), center(fd) {
    fread_be (&alpha, sizeof(double), 1, fd) ;
    do_coloc() ;
}
 
// Destructor
Domain_polar_nucleus::~Domain_polar_nucleus() {}
 
void Domain_polar_nucleus::save (FILE* fd) const {
    nbr_points.save(fd) ;
    nbr_coefs.save(fd) ;
    fwrite_be (&ndim, sizeof(int), 1, fd) ;
    fwrite_be (&type_base, sizeof(int), 1, fd) ;
    center.save(fd) ;
    fwrite_be (&alpha, sizeof(double), 1, fd) ;
}
 
ostream& Domain_polar_nucleus::print (ostream& o) const {
  o << "Polar nucleus" << endl ;
  o << "Rmax    = " << alpha << endl ;
  o << "Center  = " << center << endl ;
  o << "Nbr pts = " << nbr_points << endl ;
  o << endl ;
  return o ;
}
 
 
Val_domain Domain_polar_nucleus::der_normal (const Val_domain& so, int bound) const {
 
    Val_domain res (so.der_var(1)) ;
    switch (bound) {
        case OUTER_BC :
            res /= alpha ;
            break ;
        default:
            cerr << "Unknown boundary case in Domain_polar_nucleus::der_normal" << endl ;
            abort() ;
        }
return res ;
}
 
// Computes the cartesian coordinates
void Domain_polar_nucleus::do_absol () const {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<2 ; i++)
       assert (absol[i] == 0x0) ;
    for (int i=0 ; i<2 ; i++) {
       absol[i] = new Val_domain(this) ;
       absol[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
        absol[0]->set(index) = alpha* ((*coloc[0])(index(0))) *
             sin((*coloc[1])(index(1))) + center(1);
        absol[1]->set(index) = alpha* ((*coloc[0])(index(0))) * cos((*coloc[1])(index(1))) + center(2) ;
    }
    while (index.inc())  ;
    
}
 
// Computes the radius
void Domain_polar_nucleus::do_radius ()  const {
 
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != 0x0) ;
    assert (radius == 0x0) ;
    radius = new Val_domain(this) ;
    radius->allocate_conf() ;
    Index index (nbr_points) ;
    do
        radius->set(index) = alpha* ((*coloc[0])(index(0))) ;
    while (index.inc())  ;
}
 
// Computes the cartesian coordinates
void Domain_polar_nucleus::do_cart () const {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<2 ; i++)
       assert (cart[i] == 0x0) ;
    for (int i=0 ; i<2 ; i++) {
       cart[i] = new Val_domain(this) ;
       cart[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
        cart[0]->set(index) = alpha* ((*coloc[0])(index(0))) *
             sin((*coloc[1])(index(1))) + center(1);
        cart[1]->set(index) = alpha* ((*coloc[0])(index(0))) * cos((*coloc[1])(index(1))) + center(2) ;
    }
    while (index.inc())  ;
    
}
 
// Computes the cartesian coordinates over the radius 
void Domain_polar_nucleus::do_cart_surr () const {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<2 ; i++)
       assert (cart_surr[i] == 0x0) ;
    for (int i=0 ; i<2 ; i++) {
       cart_surr[i] = new Val_domain(this) ;
       cart_surr[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
        cart_surr[0]->set(index) = sin((*coloc[1])(index(1))) + center(1);
        cart_surr[1]->set(index) = cos((*coloc[1])(index(1))) + center(2) ;
    }
    while (index.inc())  ;
    
}
 
// Is a point inside this domain ?
bool Domain_polar_nucleus::is_in (const Point& xx, double prec) const {
 
    assert (xx.get_ndim()==2) ;
    
    double rho_loc = xx(1) - center(1) ;
    double z_loc = xx(2) - center(2) ;
    double air_loc = sqrt (rho_loc*rho_loc + z_loc*z_loc) ;
    
    bool res = (air_loc <= alpha+prec) ? true : false ;
    return res ;
}
 
// Convert absolute coordinates to numerical ones
const Point Domain_polar_nucleus::absol_to_num(const Point& abs) const {
 
    assert (is_in(abs)) ;
    Point num(2) ;
    
    double rho_loc = fabs(abs(1) - center(1)) ;
    double z_loc = abs(2) - center(2) ;
    double air = sqrt(rho_loc*rho_loc+z_loc*z_loc) ;
    num.set(1) = air/alpha ;
    
    if (rho_loc==0) {
        // Sur l'axe
        num.set(2) = (z_loc>=0) ? 0 : M_PI ;
    }
    else {
        num.set(2) = atan(rho_loc/z_loc) ;
        }   
    
    if (num(2) <0)
        num.set(2) = M_PI + num(2) ;
    
    return num ;
}
 
double coloc_leg_parity(int, int) ;
void Domain_polar_nucleus::do_coloc () {
 
    switch (type_base) {
        case CHEB_TYPE:
            nbr_coefs = nbr_points ;
            del_deriv() ;
            for (int i=0 ; i<ndim ; i++)
                coloc[i] = new Array<double> (nbr_points(i)) ;
            for (int i=0 ; i<nbr_points(0) ; i++)
                coloc[0]->set(i) = sin(M_PI/2.*i/(nbr_points(0)-1)) ;
            for (int j=0 ; j<nbr_points(1) ; j++)
                coloc[1]->set(j) = M_PI/2.*j/(nbr_points(1)-1) ;
            break ;
        case LEG_TYPE:
            nbr_coefs = nbr_points ;
            del_deriv() ;
            for (int i=0 ; i<ndim ; i++) 
                coloc[i] = new Array<double> (nbr_points(i)) ;
            for (int i=0 ; i<nbr_points(0) ; i++)
                coloc[0]->set(i) = coloc_leg_parity(i, nbr_points(0)) ;
            for (int j=0 ; j<nbr_points(1) ; j++)
                coloc[1]->set(j) = M_PI/2.*j/(nbr_points(1)-1) ;
            break ;
        default :
            cerr << "Unknown type of basis in Domain_polar_nucleus::do_coloc" << endl ;
            abort() ;
    }
}
 
// Base for a function symetric in z, using Chebyshev
void Domain_polar_nucleus::set_cheb_base(Base_spectral& base) const {
  set_cheb_base_with_m (base, 0) ;
}
 
// Base for a function anti-symetric in z, using Chebyshev
void Domain_polar_nucleus::set_anti_cheb_base(Base_spectral& base) const {
  set_anti_cheb_base_with_m(base, 0) ;
}
 
// Base for a function symetric in z, using Legendre
void Domain_polar_nucleus::set_legendre_base(Base_spectral& base) const  {
  set_legendre_base_with_m(base, 0) ;
 }
 
// Base for a function anti-symetric in z, using Legendre
void Domain_polar_nucleus::set_anti_legendre_base(Base_spectral& base) const  {
      set_anti_legendre_base_with_m(base, 0) ;
 }
 
// Base for a function symetric in z, using Chebyshev
void Domain_polar_nucleus::set_cheb_base_with_m(Base_spectral& base, int m) const {
 
    int l ;
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[1]->set(0) = (m%2==0) ? COS_EVEN : SIN_ODD ;
    for (int j=0 ; j<nbr_coefs(1) ; j++) {
        l = (m%2==0) ? 2*j : 2*j+1 ;    
        base.bases_1d[0]->set(j) = (l%2==0) ? CHEB_EVEN : CHEB_ODD ;
         }
}
 
// Base for a function anti-symetric in z, using Chebyshev
void Domain_polar_nucleus::set_anti_cheb_base_with_m(Base_spectral& base, int m) const {
 
    int l ;
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[1]->set(0) = (m%2==0) ? COS_ODD : SIN_EVEN ;
    for (int j=0 ; j<nbr_coefs(1) ; j++) {
      l = (m%2==0) ? 2*j+1 : 2*j ;    
      base.bases_1d[0]->set(j) = (l%2==1) ? CHEB_ODD : CHEB_EVEN ;
    }
}
 
// Base for a function symetric in z, using Legendre
void Domain_polar_nucleus::set_legendre_base_with_m(Base_spectral& base, int m) const  {
 
    int l ;
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def = true ;
    base.bases_1d[1]->set(0) = (m%2==0) ? COS_EVEN : SIN_ODD ;
    for (int j=0 ; j<nbr_coefs(1) ; j++) {
      l = (m%2==0) ? 2*j : 2*j+1 ;    
      base.bases_1d[0]->set(j) = (l%2==0) ? LEG_EVEN : LEG_ODD ;
    }
 }
 
// Base for a function anti-symetric in z, using Legendre
void Domain_polar_nucleus::set_anti_legendre_base_with_m(Base_spectral& base, int m) const  {
      
    int l ;
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def = true ;
    base.bases_1d[1]->set(0) = (m%2==0) ? COS_ODD : SIN_EVEN ;
    for (int j=0 ; j<nbr_coefs(1) ; j++) {
      l = (m%2==0) ? 2*j+1 : 2*j ;    
      base.bases_1d[0]->set(j) = (l%2==1) ? LEG_ODD : LEG_EVEN ;
    }
 }
 
// Computes the derivatives with respect to rho,Z as a function of the numerical ones.
void Domain_polar_nucleus::do_der_abs_from_der_var(const Val_domain *const *const der_var, Val_domain **const der_abs) const {
    Val_domain dr (*der_var[0]/alpha) ;
    Val_domain dtsr (der_var[1]->div_x()/alpha) ;
 
    // D / drho
    der_abs[0] = new Val_domain (dr.mult_sin_theta() + dtsr.mult_cos_theta()) ;
    // d/dz :
    der_abs[1] = new Val_domain (dr.mult_cos_theta() - dtsr.mult_sin_theta()) ;
}
 
// Rules for the multiplication of two basis.
Base_spectral Domain_polar_nucleus::mult (const Base_spectral& a, const Base_spectral& b) const {
 
    assert (a.ndim==2) ;
    assert (b.ndim==2) ;
    
    Base_spectral res(2) ;
    bool res_def = true ;
 
    if (!a.def)
        res_def=false ;
    if (!b.def)
        res_def=false ;
        
    if (res_def) {
 
 
    // Bases in theta :
    res.bases_1d[1] = new Array<int> (a.bases_1d[1]->get_dimensions()) ;
    switch ((*a.bases_1d[1])(0)) {
        case COS_EVEN:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) = SIN_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = SIN_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case COS_ODD:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) =  SIN_ODD  ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = SIN_EVEN  ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_EVEN:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = SIN_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = SIN_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_ODD:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = SIN_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = SIN_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
    }
 
    // Base in r :
    Index index_0 (a.bases_1d[0]->get_dimensions()) ;
    res.bases_1d[0] = new Array<int> (a.bases_1d[0]->get_dimensions()) ;
    do {
    switch ((*a.bases_1d[0])(index_0)) {
        case CHEB_EVEN:
            switch ((*b.bases_1d[0])(index_0)) {
                case CHEB_EVEN:
                    res.bases_1d[0]->set(index_0) = CHEB_EVEN ;
                    break ;
                case CHEB_ODD:
                    res.bases_1d[0]->set(index_0) = CHEB_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case CHEB_ODD:
            switch ((*b.bases_1d[0])(index_0)) {
                case CHEB_EVEN:
                    res.bases_1d[0]->set(index_0) = CHEB_ODD ;
                    break ;
                case CHEB_ODD:
                    res.bases_1d[0]->set(index_0) = CHEB_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case LEG_EVEN:
            switch ((*b.bases_1d[0])(index_0)) {
                case LEG_EVEN:
                    res.bases_1d[0]->set(index_0) = LEG_EVEN  ;
                    break ;
                case LEG_ODD:
                    res.bases_1d[0]->set(index_0) = LEG_ODD  ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case LEG_ODD:
            switch ((*b.bases_1d[0])(index_0)) {
                case LEG_EVEN:
                    res.bases_1d[0]->set(index_0) = LEG_ODD  ;
                    break ;
                case LEG_ODD:
                    res.bases_1d[0]->set(index_0) = LEG_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
        }
    }
    while (index_0.inc()) ;
    }
    if (!res_def) 
        for (int dim=0 ; dim<a.ndim ; dim++)
            if (res.bases_1d[dim]!= 0x0) {
                delete res.bases_1d[dim] ;
                res.bases_1d[dim] = 0x0 ;
                }
    res.def = res_def ;
    return res ;
}
 
int Domain_polar_nucleus::give_place_var (char* p) const {
    int res = -1 ;
    if (strcmp(p,"R ")==0)
    res = 0 ;
    if (strcmp(p,"T ")==0)
    res = 1 ;
    return res ;
}
}