domain_compact_ope.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 "spheric.hpp"
#include "val_domain.hpp"
#include "array_math.hpp"
namespace Kadath {
int mult_cos_1d (int, Array<double>&) ;
int mult_sin_1d (int, Array<double>&) ;
int div_sin_1d (int, Array<double>&) ;
int div_cos_1d (int, Array<double>&) ;
int div_xm1_1d (int, Array<double>&) ;
int mult_xm1_1d (int, Array<double>&) ;
 
Val_domain Domain_compact::mult_cos_phi (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base.allocate (nbr_coefs) ; 
    *res.base.bases_1d[2] = *so.base.bases_1d[2] ;
    
    Index index_t (res.base.bases_1d[1]->get_dimensions()) ;
    // Inversion in theta :
    do {
        switch ((*so.base.bases_1d[1])(index_t)) {
            case COS_EVEN :
                res.base.bases_1d[1]->set(index_t) = SIN_ODD ;
                break ;
            case COS_ODD :
                res.base.bases_1d[1]->set(index_t) = SIN_EVEN ;
                break ;
            case SIN_EVEN :
                res.base.bases_1d[1]->set(index_t) = COS_ODD ;
                break ;
            case SIN_ODD :
                res.base.bases_1d[1]->set(index_t) = COS_EVEN ;
                break ;
                default : 
                    cout << "Unknown case in Domain_compact::mult_cos_phi" << endl ;
                    abort() ;
                }
        }
    while (index_t.inc()) ;
    *res.base.bases_1d[0] = *so.base.bases_1d[0] ;
 
    res.base.def = true ;
 
    res.cf = new Array<double> (so.base.ope_1d(mult_cos_1d, 2, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::mult_sin_phi (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base.allocate (nbr_coefs) ; 
    *res.base.bases_1d[2] = *so.base.bases_1d[2] ;
    
    Index index_t (res.base.bases_1d[1]->get_dimensions()) ;
    // Inversion in theta :
    do {
        switch ((*so.base.bases_1d[1])(index_t)) {
            case COS_EVEN :
                res.base.bases_1d[1]->set(index_t) = SIN_ODD ;
                break ;
            case COS_ODD :
                res.base.bases_1d[1]->set(index_t) = SIN_EVEN ;
                break ;
            case SIN_EVEN :
                res.base.bases_1d[1]->set(index_t) = COS_ODD ;
                break ;
            case SIN_ODD :
                res.base.bases_1d[1]->set(index_t) = COS_EVEN ;
                break ;
                default : 
                    cout << "Unknown case in Domain_compact::mult_sin_phi" << endl ;
                    abort() ;
                }
        }
    while (index_t.inc()) ;
    *res.base.bases_1d[0] = *so.base.bases_1d[0] ;
 
    res.base.def = true ;
 
    res.cf = new Array<double> (so.base.ope_1d(mult_sin_1d, 2, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::mult_cos_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(mult_cos_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::mult_sin_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    
    res.cf = new Array<double> (so.base.ope_1d(mult_sin_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::div_sin_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(div_sin_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::div_cos_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(div_cos_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::mult_xm1 (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    
    res.cf = new Array<double> (so.base.ope_1d(mult_xm1_1d, 0, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::div_xm1 (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(div_xm1_1d, 0, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_compact::mult_r (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(div_xm1(so)) ;
    res /= alpha ;
    return res ;
}
 
Val_domain Domain_compact::div_r (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(mult_xm1(so)) ;
    res *= alpha ;
    return res ;
}
 
Val_domain Domain_compact::der_r (const Val_domain& so) const {
  return (-alpha*so.der_var(1).mult_xm1().mult_xm1()) ;
}
 
Val_domain Domain_compact::der_r_rtwo (const Val_domain& so) const {
  return (-so.der_var(1)/alpha) ;
}
 
Val_domain Domain_compact::dt (const Val_domain& so) const {
  return (so.der_var(2)) ;
}
 
 
Val_domain Domain_compact::der_partial_var (const Val_domain& so, int which_var) const {
 
    switch (which_var) {
        case 0 :
            return so.der_r() ;
            break ;
        case 1 : 
            return so.der_var(2) ;
            break ;
        case 2 :
            return so.der_var(3) ;
        default:
            cerr << "Unknown variable in Domain_compact::der_partial_var" << endl ;
            abort() ;
        }
}
 
Val_domain Domain_compact::laplacian2 (const Val_domain& so, int m) const {
  Val_domain derr (-alpha*so.der_var(1).mult_xm1().mult_xm1()) ;
  Val_domain dderr (-alpha*derr.der_var(1).mult_xm1().mult_xm1()) ;
  Val_domain dert (so.der_var(2)) ;
  Val_domain res (dderr + div_r(derr + div_r(dert.der_var(2)))) ;
  if (m!=0)
    res -= m * m * div_r(div_r(so.div_sin_theta().div_sin_theta())) ;
  return res ;
}
 
double integral_1d (int, const Array<double>&) ;
double Domain_compact::integ_volume (const Val_domain& so) const {
  
 if (so.check_if_zero())
   return 0 ;
 else {
 Val_domain integrant (-mult_r(mult_r(mult_r(mult_r(mult_sin_theta(so)))))*alpha) ;
 integrant.coef() ;
 
 double val = 0 ;
 // Only k = 0
 int baset = (*integrant.get_base().bases_1d[1]) (0) ;
 assert(baset==SIN_ODD) ;
 Index pos (nbr_coefs) ;
 for (int j=0 ; j<nbr_coefs(1) ; j++) {
   pos.set(1) = j ;
  int baser = (*integrant.get_base().bases_1d[0]) (j, 0) ;
  assert (baser==CHEB) ;
 
  Array<double> cf (nbr_coefs(0)) ;
  for (int i=0 ; i<nbr_coefs(0) ; i++) {
    pos.set(0) = i ;
    cf.set(i) = integrant.get_coef(pos) ;
  }
  val += 2./(2.*j+1) * integral_1d(CHEB, cf) ;
 }
 
 return val * 2*M_PI ; 
}
}
}