domain_polar_outer_adapted.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 "utilities.hpp"
#include "adapted_polar.hpp"
#include "point.hpp"
#include "array_math.hpp"
#include "val_domain.hpp"
#include "scalar.hpp"
#include "tensor_impl.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_shell_outer_adapted::Domain_polar_shell_outer_adapted (const Space& sss, int num, int ttype, double rin, double rout, const Point& cr, const Dim_array& nbr) :  
        Domain(num, ttype, nbr), sp(sss), inner_radius(rin), center(cr) {
     assert (nbr.get_ndim()==2) ;
     assert (cr.get_ndim()==2) ;
     
    
     outer_radius_term_eq = nullptr ;
     rad_term_eq = nullptr ;
     der_rad_term_eq = nullptr ; 
     dt_rad_term_eq = nullptr ;    
     normal_spher = nullptr ;
     normal_cart = nullptr ;
     
     do_coloc() ; 
     outer_radius = new Val_domain (this) ;
     *outer_radius = rout ;
     outer_radius->std_base() ;
}
 
Domain_polar_shell_outer_adapted::Domain_polar_shell_outer_adapted (const Space& sss, int num, int ttype,  double rin, const Val_domain& rout, const Point& cr, const Dim_array& nbr) :  
        Domain(num, ttype, nbr), sp(sss), inner_radius(rin), center(cr) {
     assert (nbr.get_ndim()==2) ;
     assert (cr.get_ndim()==2) ;
     
    
     outer_radius_term_eq = nullptr ;
     rad_term_eq = nullptr ;
     der_rad_term_eq = nullptr ; 
     dt_rad_term_eq = nullptr ;    
     normal_spher = nullptr ;
     normal_cart = nullptr ;
       
     do_coloc() ; 
     outer_radius = new Val_domain(rout) ;
}
 
// Constructor by copy
Domain_polar_shell_outer_adapted::Domain_polar_shell_outer_adapted (const Domain_polar_shell_outer_adapted& so) : Domain(so), sp(so.sp),
          inner_radius (so.inner_radius), center(so.center) {
  
  outer_radius = new Val_domain (*so.outer_radius) ;
  if (so.outer_radius_term_eq != nullptr)
      outer_radius_term_eq = new Term_eq (*so.outer_radius_term_eq) ;
  if (so.rad_term_eq !=nullptr)
    rad_term_eq = new Term_eq (*so.rad_term_eq) ;
  if (so.der_rad_term_eq !=nullptr)
    der_rad_term_eq = new Term_eq (*so.der_rad_term_eq) ; 
  if (so.dt_rad_term_eq !=nullptr)
    dt_rad_term_eq = new Term_eq (*so.dt_rad_term_eq) ;  
  if (so.normal_spher !=nullptr)
    normal_spher = new Term_eq (*so.normal_spher) ; 
  if (so.normal_cart !=nullptr)
    normal_cart = new Term_eq (*so.normal_cart) ;
}
 
Domain_polar_shell_outer_adapted::Domain_polar_shell_outer_adapted (const Space& sss, int num, FILE* fd) : Domain(num, fd), sp(sss), center(fd) {
    fread_be (&inner_radius, sizeof(double), 1, fd) ;
        outer_radius = new Val_domain(this, fd) ;
    
    outer_radius_term_eq = nullptr ;
    rad_term_eq = nullptr ;
    der_rad_term_eq = nullptr ;  
    dt_rad_term_eq = nullptr ;    
    normal_spher = nullptr ;
        normal_cart = nullptr ;
    
    do_coloc() ;
}
 
void Domain_polar_shell_outer_adapted::do_radius () const  {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != nullptr) ;
    assert (radius == nullptr) ;
    radius = new Val_domain(this) ;
    radius->allocate_conf() ;
    Index index (nbr_points) ;
    do 
        radius->set(index) = ((*outer_radius)(index) - inner_radius)/2.* ((*coloc[0])(index(0))) + ((*outer_radius)(index) + inner_radius)/2. ;
    while (index.inc())  ;
    radius->std_r_base() ;
}
 
// Destructor
Domain_polar_shell_outer_adapted::~Domain_polar_shell_outer_adapted() {
 
  delete outer_radius ;
  if (outer_radius_term_eq != nullptr)
      delete outer_radius_term_eq ;
  if (rad_term_eq != nullptr)
      delete rad_term_eq ;
  if (der_rad_term_eq != nullptr)
      delete der_rad_term_eq ;  
  if (normal_spher != nullptr)
      delete normal_spher ;
   if (normal_cart != nullptr)
      delete normal_cart ;
   if (dt_rad_term_eq != nullptr)
      delete dt_rad_term_eq ;  
}
 
void Domain_polar_shell_outer_adapted::del_deriv() {
    safe_delete(outer_radius_term_eq);
    safe_delete(rad_term_eq);
    safe_delete(der_rad_term_eq);
    safe_delete(normal_spher);
    safe_delete(normal_cart);
    safe_delete(dt_rad_term_eq);
}
 
 
int Domain_polar_shell_outer_adapted::nbr_unknowns_from_adapted() const {
  return nbr_coefs(1) ;
}
 
void Domain_polar_shell_outer_adapted::vars_to_terms() const {
 
  if (outer_radius_term_eq != nullptr)
      delete outer_radius_term_eq ;
  Scalar val (sp) ;
  val.set_domain(num_dom) = *outer_radius ;
  
  outer_radius_term_eq = new Term_eq (num_dom, val) ;
  update() ;
}
 
void Domain_polar_shell_outer_adapted::affecte_coef(int& conte, int cc, bool& found) const {
 
    Val_domain auxi (this) ;
    auxi.std_base() ;
    auxi.set_in_coef() ;
    auxi.allocate_coef() ;
    *auxi.cf = 0 ;
    
    found = false ;
    
    
     for (int j=0 ; j<nbr_coefs(1) ; j++) {
          if (conte==cc) {
          Index pos_cf (nbr_coefs) ;
          pos_cf.set(0) = 0 ;
          pos_cf.set(1) = j ;
          auxi.cf->set(pos_cf) = 1 ;
          found = true ;
          }
          conte ++ ;
      }
      
      if (found) {
    Scalar auxi_scal (sp) ;
    auxi_scal.set_domain(num_dom) = auxi ;
    outer_radius_term_eq->set_der_t(auxi_scal) ;
      }
      else {
    outer_radius_term_eq->set_der_zero() ;
      }
    update() ;
}
 
void Domain_polar_shell_outer_adapted::xx_to_vars_from_adapted(Val_domain& new_outer_radius, const Array<double>& xx, int& pos) const {
 
    new_outer_radius.allocate_coef() ;
    *new_outer_radius.cf = 0 ;
    
    Index pos_cf (nbr_coefs) ;      
    pos_cf.set(0) = 0 ;
    
      for (int j=0 ; j<nbr_coefs(1) ; j++) {
        pos_cf.set(1)=  j ;
        new_outer_radius.cf->set(pos_cf) -= xx(pos) ; 
        pos ++ ;
      }
      
      new_outer_radius.set_base() = outer_radius->get_base() ;  
}
 
void Domain_polar_shell_outer_adapted::update_mapping (const Val_domain& cor) {
 
  *outer_radius += cor ;
  for (int l=0 ; l<ndim ; l++) {
        if (absol[l] !=nullptr) delete absol[l] ;
        if (cart[l] !=nullptr) delete cart[l] ;
        if (cart_surr[l] !=nullptr) delete cart_surr[l] ;
        absol[l] = nullptr ;
        cart_surr[l] = nullptr ;
        cart[l]=  nullptr ;
    }
    if (radius !=nullptr)
        delete radius ;
    radius = nullptr ;
  update() ;
}
 
void Domain_polar_shell_outer_adapted::set_mapping (const Val_domain& cor) const {
 
  *outer_radius = cor ;
  for (int l=0 ; l<ndim ; l++) {
        if (absol[l] !=nullptr) delete absol[l] ;
        if (cart[l] !=nullptr) delete cart[l] ;
        if (cart_surr[l] !=nullptr) delete cart_surr[l] ;
        absol[l] = nullptr ;
        cart_surr[l] = nullptr ;
        cart[l]=  nullptr ;
    }
    if (radius !=nullptr)
        delete radius ;
    radius = nullptr ;
  vars_to_terms() ;
}
 
void Domain_polar_shell_outer_adapted::update_variable (const Val_domain& cor_outer_radius, const Scalar& old, Scalar& res) const {
  
      Val_domain dr (old(num_dom).der_r()) ;
      if (dr.check_if_zero()) 
     res.set_domain(num_dom) = 0 ;
      else {
      
      Index pos(nbr_points) ;
      res.set_domain(num_dom).allocate_conf() ;
      do {
      res.set_domain(num_dom).set(pos) = dr(pos) * (1+(*coloc[0])(pos(0))) / 2. ;
      }
      while (pos.inc()) ;
      
      res.set_domain(num_dom) = cor_outer_radius * res(num_dom) + old(num_dom) ; 
      res.set_domain(num_dom).set_base() = old(num_dom).get_base() ;
      }
}
 
 
void Domain_polar_shell_outer_adapted::xx_to_ders_from_adapted(const Array<double>& xx, int& pos) const {
 
    Val_domain auxi (this) ;
    auxi.std_base() ;
    auxi.set_in_coef() ;
    auxi.allocate_coef() ;
    *auxi.cf = 0 ;
    
    Index pos_cf (nbr_coefs) ;      
    pos_cf.set(0) = 0 ;
   
      for (int j=0 ; j<nbr_coefs(1) ; j++) {
        pos_cf.set(1)=  j ;
        auxi.cf->set(pos_cf) = xx(pos) ;
        pos ++ ;
      }
 
     Scalar auxi_scal (sp) ;
     auxi_scal.set_domain(num_dom) = auxi ;
     outer_radius_term_eq->set_der_t(auxi_scal) ;
     update() ;
}
 
 
void Domain_polar_shell_outer_adapted::update() const {
 
  if (rad_term_eq != nullptr)
      delete rad_term_eq ;
  if (der_rad_term_eq != nullptr)
      delete der_rad_term_eq ;  
    if (dt_rad_term_eq != nullptr)
      delete dt_rad_term_eq ;  
 
  // Computation of rad_term_eq
  Scalar val_res (sp) ;
  val_res.set_domain(num_dom).allocate_conf() ;
  Index index (nbr_points) ;
  do  {
    val_res.set_domain(num_dom).set(index) =  (((*outer_radius_term_eq->val_t)()(num_dom))(index) - inner_radius )/2. * ((*coloc[0])(index(0))) + 
              (((*outer_radius_term_eq->val_t)()(num_dom))(index) + inner_radius )/2.   ;
    }
    while (index.inc())  ;
  val_res.set_domain(num_dom).std_r_base() ;
  
  bool doder = (outer_radius_term_eq->der_t ==nullptr) ? false : true ;
  if (doder) {
      Scalar der_res (sp) ; 
      if ((*outer_radius_term_eq->der_t)()(num_dom).check_if_zero()) {
    der_res.set_domain(num_dom).set_zero() ;
      }
      else {
      der_res.set_domain(num_dom).allocate_conf() ;
      index.set_start() ;
      do  {
    der_res.set_domain(num_dom).set(index) = ((*outer_radius_term_eq->der_t)()(num_dom))(index)/2. * ((*coloc[0])(index(0))) + 
                      ((*outer_radius_term_eq->der_t)()(num_dom))(index)/2.   ;
    }
    while (index.inc())  ;
    der_res.set_domain(num_dom).std_r_base() ;
      }
  rad_term_eq = new Term_eq (num_dom, val_res, der_res) ;  
  }
  else
     rad_term_eq = new Term_eq (num_dom, val_res) ;
  
  // Computation of der_rad_term_eq which is dr / dxi 
  val_res.set_domain(num_dom) = ((*outer_radius_term_eq->val_t)()(num_dom)-inner_radius) / 2.  ;
  if (doder) {
      Scalar der_res (sp) ;
      der_res.set_domain(num_dom) = (*outer_radius_term_eq->der_t)()(num_dom) / 2. ;
      der_rad_term_eq = new Term_eq (num_dom, val_res, der_res) ;
  }
  else
    der_rad_term_eq = new Term_eq (num_dom, val_res) ;
  
   // Computation of dt_rad_term_eq which is dr / d theta
  val_res.set_domain(num_dom) = (*rad_term_eq->val_t)()(num_dom).der_var(2) ;
  if (doder) {
      Scalar der_res (sp) ;
      der_res.set_domain(num_dom) = (*rad_term_eq->der_t)()(num_dom).der_var(2) ;
      dt_rad_term_eq = new Term_eq (num_dom, val_res, der_res) ;
  }
  else
    dt_rad_term_eq = new Term_eq (num_dom, val_res) ;
  
  do_normal_cart() ;
}
 
void Domain_polar_shell_outer_adapted::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 (&inner_radius, sizeof(double), 1, fd) ;
    outer_radius->save(fd) ;
}
 
ostream& Domain_polar_shell_outer_adapted::print (ostream& o) const {
  o << "Adapted polar shell on the inside boundary" << endl ;
  o << "Center  = " << center << endl ;
  o << "Nbr pts = " << nbr_points << endl ;
  o << "Inner radius " << inner_radius << endl ;
  o << "Outer radius " << endl ;
  o << *outer_radius << endl ;
  o << endl ;
  return o ;
}
 
 
 
Val_domain Domain_polar_shell_outer_adapted::der_normal (const Val_domain&, int) const {
    cerr << "Domain_polar_shell_outer_adapted::der_normal not implemeted" << endl ;
    abort() ;
}
 
// Computes the cartesian coordinates
void Domain_polar_shell_outer_adapted::do_absol () const {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != nullptr) ;
    for (int i=0 ; i<2 ; i++)
       assert (absol[i] == nullptr) ;
    for (int i=0 ; i<2 ; i++) {
       absol[i] = new Val_domain(this) ;
       absol[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
      
        double rr = ((*outer_radius)(index) - inner_radius)/2. * ((*coloc[0])(index(0))) + 
                ((*outer_radius)(index) + inner_radius)/2. ;
        absol[0]->set(index) = rr *
             sin((*coloc[1])(index(1))) + center(1);
        absol[1]->set(index) = rr * cos((*coloc[1])(index(1))) + center(2) ;
    }
    while (index.inc())  ;
    
}
 
// Computes the cartesian coordinates
void Domain_polar_shell_outer_adapted::do_cart () const {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != nullptr) ;
    for (int i=0 ; i<2 ; i++)
       assert (cart[i] == nullptr) ;
    for (int i=0 ; i<2 ; i++) {
       cart[i] = new Val_domain(this) ;
       cart[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
        double rr = ((*outer_radius)(index) - inner_radius)/2. * ((*coloc[0])(index(0))) + 
                ((*outer_radius)(index) + inner_radius)/2. ;
        cart[0]->set(index) = rr *
             sin((*coloc[1])(index(1))) + center(1);
        cart[1]->set(index) = rr * cos((*coloc[1])(index(1))) + center(2) ;
    }
    while (index.inc())  ;
    
}
 
 
// Computes the cartesian coordinates over the radius 
void Domain_polar_shell_outer_adapted::do_cart_surr () const {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != nullptr) ;
    for (int i=0 ; i<2 ; i++)
       assert (cart_surr[i] == nullptr) ;
    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))) ;
        cart_surr[1]->set(index) = cos((*coloc[1])(index(1)))  ;
    }
    while (index.inc())  ;
    
}
 
 
// Is a point inside this domain ?
bool Domain_polar_shell_outer_adapted::is_in (const Point& xx, double prec) const {
    
    assert (xx.get_ndim()==2) ;
    Point num (absol_to_num(xx)) ;
    bool res = ((num(1)>-1-prec) && (num(1)<1+prec)) ? true : false ;
    return res ;
}
 
 
// Convert absolute coordinates to numerical ones
const Point Domain_polar_shell_outer_adapted::absol_to_num(const Point& abs) const {
        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) ;
        
    if (rho_loc==0) {
        // On the axis ?
        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) ;
    
    // Get the boundary for those angles
    num.set(1) = 1 ;
    outer_radius->coef() ;
    double outer = outer_radius->get_base().summation(num, outer_radius->get_coef()) ;
    num.set(1) = (2./(outer-inner_radius)) * (air - (outer + inner_radius)/2.) ;
    
    return num ;
}
 
 
double coloc_leg(int, int) ;
void Domain_polar_shell_outer_adapted::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) = -cos(M_PI*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(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_shell_outer_adapted::do_coloc" << endl ;
            abort() ;
    }
}
 
void Domain_polar_shell_outer_adapted::set_cheb_base(Base_spectral& base) const  {
  set_cheb_base_with_m(base, 0) ;
}
 
// standard base for a anti-symetric function in z, using Chebyshev
void Domain_polar_shell_outer_adapted::set_anti_cheb_base(Base_spectral& base) const  {
  set_anti_cheb_base_with_m(base, 0) ;
}
 
// standard base for a symetric function in z, using Legendre
void Domain_polar_shell_outer_adapted::set_legendre_base(Base_spectral& base) const {
  set_legendre_base_with_m(base, 0) ;
}
 
// standard base for a anti-symetric function in z, using Legendre
void Domain_polar_shell_outer_adapted::set_anti_legendre_base(Base_spectral& base) const {
  set_anti_legendre_base_with_m(base, 0) ;
}
 
 
// standard base for a symetric function in z, using Chebyshev
void Domain_polar_shell_outer_adapted::set_cheb_base_with_m(Base_spectral& base, int m) const  {
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    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++)
      base.bases_1d[0]->set(j) = CHEB ;
}
 
// standard base for a anti-symetric function in z, using Chebyshev
void Domain_polar_shell_outer_adapted::set_anti_cheb_base_with_m(Base_spectral& base, int m) const  {
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    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++)
      base.bases_1d[0]->set(j) = CHEB ;
}
 
// standard base for a symetric function in z, using Legendre
void Domain_polar_shell_outer_adapted::set_legendre_base_with_m(Base_spectral& base, int m) const {
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    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++)
      base.bases_1d[0]->set(j) = LEG ;
}
 
// standard base for a anti-symetric function in z, using Legendre
void Domain_polar_shell_outer_adapted::set_anti_legendre_base_with_m(Base_spectral& base, int m) const {
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    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++)
      base.bases_1d[0]->set(j) = LEG ;
}
 
 
void Domain_polar_shell_outer_adapted::set_cheb_r_base(Base_spectral& base) const  {
 set_cheb_base_with_m(base, 0) ;
}
 
void Domain_polar_shell_outer_adapted::set_legendre_r_base(Base_spectral& base) const  {
 set_legendre_base_with_m(base, 0) ;
}
 
// Computes the derivatives with respect to XYZ as a function of the numerical ones.
void Domain_polar_shell_outer_adapted::do_der_abs_from_der_var(const Val_domain *const *const der_var, Val_domain **const der_abs) const {
    Val_domain rr (get_radius()) ;
    Val_domain dr (*der_var[0] / (*der_rad_term_eq->val_t)()(num_dom)) ;
    Val_domain dtsr ((*der_var[1] - rr.der_var(2) * dr) / rr);
    dtsr.set_base() = der_var[1]->get_base() ;
 
    // d/dx :
    Val_domain sintdr (dr.mult_sin_theta()) ;   
    Val_domain costdtsr (dtsr.mult_cos_theta()) ;
 
    der_abs[0] = new Val_domain (sintdr+costdtsr) ;
 
    // 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_shell_outer_adapted::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:
            switch ((*b.bases_1d[0])(index_0)) {
                case CHEB:
                    res.bases_1d[0]->set(index_0) = CHEB ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case LEG:
            switch ((*b.bases_1d[0])(index_0)) {
                case LEG:
                    res.bases_1d[0]->set(index_0) = LEG ;
                    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]!= nullptr) {
                delete res.bases_1d[dim] ;
                res.bases_1d[dim] = nullptr ;
                }
    res.def = res_def ;
    return res ;
}
 
 
 
void Domain_polar_shell_outer_adapted::update_constante (const Val_domain& cor_outer_radius, const Scalar& old, Scalar& res) const {
  
      Point MM(2) ;
      Index pos(nbr_points) ;
      res.set_domain(num_dom).allocate_conf() ;
      do {
      
      double rr = ((*outer_radius)(pos)+ cor_outer_radius(pos) - inner_radius) * (*coloc[0])(pos(0)) / 2. 
        + ((*outer_radius)(pos)+ cor_outer_radius(pos) + inner_radius) /2.;
      double theta = (*coloc[1])(pos(1)) ;
      
      MM.set(1) = rr*sin(theta) + center(1);
      MM.set(2) = rr*cos(theta) + center(2);
        
      res.set_domain(num_dom).set(pos) = old.val_point(MM, -1) ;
    
      }
      while (pos.inc()) ;
      
      res.set_domain(num_dom).set_base() = old(num_dom).get_base() ;
}
 
 
int Domain_polar_shell_outer_adapted::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 ;
}
}