dalembert.C

/*
 *   Copyright (c) 2000-2001 Jerome Novak
 *
 *   This file is part of LORENE.
 *
 *   LORENE 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 2 of the License, or
 *   (at your option) any later version.
 *
 *   LORENE 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 LORENE; if not, write to the Free Software
 *   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 */


char dalembert_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/PDE/dalembert.C,v 1.10 2008/08/27 08:51:15 jl_cornou Exp $" ;

/*
 * $Id: dalembert.C,v 1.10 2008/08/27 08:51:15 jl_cornou Exp $
 * $Log: dalembert.C,v $
 * Revision 1.10  2008/08/27 08:51:15  jl_cornou
 * Added Jacobi(0,2) polynomials
 *
 * Revision 1.9  2006/08/31 08:56:40  j_novak
 * Added the possibility to have a shift in the quantum number l in the operator.
 *
 * Revision 1.8  2004/10/05 15:44:21  j_novak
 * Minor speed enhancements.
 *
 * Revision 1.7  2004/03/01 09:57:03  j_novak
 * the wave equation is solved with Scalars. It now accepts a grid with a
 * compactified external domain, which the solver ignores and where it copies
 * the values of the field from one time-step to the next.
 *
 * Revision 1.6  2003/12/19 16:21:49  j_novak
 * Shadow hunt
 *
 * Revision 1.5  2003/07/25 08:31:20  j_novak
 * Error corrected in the case of only nucleus
 *
 * Revision 1.4  2003/06/18 08:45:27  j_novak
 * In class Mg3d: added the member get_radial, returning only a radial grid
 * For dAlembert solver: the way the coefficients of the operator are defined has been changed.
 *
 * Revision 1.3  2002/01/03 13:18:41  j_novak
 * Optimization: the members set(i,j) and operator(i,j) of class Matrice are
 * now defined inline. Matrice is a friend class of Tbl.
 *
 * Revision 1.2  2002/01/02 14:07:57  j_novak
 * Dalembert equation is now solved in the shells. However, the number of
 * points in theta and phi must be the same in each domain. The solver is not
 * completely tested (beta version!).
 *
 * Revision 1.1.1.1  2001/11/20 15:19:28  e_gourgoulhon
 * LORENE
 *
 * Revision 1.1  2000/12/04  14:24:15  novak
 * Initial revision
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Non_class_members/PDE/dalembert.C,v 1.10 2008/08/27 08:51:15 jl_cornou Exp $
 *
 */


// Header C : 
#include <math.h>

// Headers Lorene :
#include "param.h"
#include "matrice.h"
#include "map.h"
#include "base_val.h"
#include "proto.h"


        //----------------------------------------------
       //       Version Mtbl_cf
      //----------------------------------------------

/*
 * 
 * Solution de l'equation de d'Alembert
 * 
 * Entree : mapping :   le mapping affine
 *      source : les coefficients de la source 
 *          La base de decomposition doit etre Ylm
 * Sortie : renvoie les coefficients de la solution dans la meme base de 
 *      decomposition (a savoir Ylm)
 *      
 */



Mtbl_cf sol_dalembert(Param& par, const Map_af& mapping, const Mtbl_cf& source) 
{
    
  // Verifications d'usage sur les zones
  int nz = source.get_mg()->get_nzone() ;
  bool ced = (source.get_mg()->get_type_r(nz-1) == UNSURR ) ;
  int nz0 = (ced ? nz - 1 : nz ) ;
  assert ((source.get_mg()->get_type_r(0) == RARE)||(source.get_mg()->get_type_r(0) == FINJAC)) ;
  for (int l=1 ; l<nz0 ; l++) {
    assert(source.get_mg()->get_type_r(l) == FIN) ;
    assert(source.get_mg()->get_nt(l) == source.get_mg()->get_nt(0)) ;
    assert(source.get_mg()->get_np(l) == source.get_mg()->get_np(0)) ;
  } // Same number of points in theta and phi in all domains...
  assert (par.get_n_double() > 0) ;
  assert (par.get_n_tbl_mod() > 1) ;
  
  //Is there a shift in the quantum number l?
  int dl = 0 ;  //value of the shift
  int l_min = 0 ; //the wave equation is solved only for l+dl >= l_min
  if (par.get_n_int() > 1) {
      dl = -1 ;
      l_min = par.get_int(1) ;
  }

  // Bases spectrales
  const Base_val& base = source.base ;
  
  // donnees sur la zone
  int nr, nt, np ;
  int base_r, type_dal ;
  double alpha, beta ;
  int l_quant, m_quant;
  nt = source.get_mg()->get_nt(0) ;
  np = source.get_mg()->get_np(0) ;
  
  //Rangement des valeurs intermediaires 
  Tbl *so ;
  Tbl *sol_hom ;
  Tbl *sol_hom2 ;
  Tbl *sol_part ;
  
  // Rangement des solutions, avant raccordement
  Mtbl_cf solution_part(source.get_mg(), base) ;
  Mtbl_cf solution_hom_un(source.get_mg(), base) ;
  Mtbl_cf solution_hom_deux(source.get_mg(), base) ;
  Mtbl_cf resultat(source.get_mg(), base) ;
  
  solution_part.set_etat_qcq() ;
  solution_hom_un.set_etat_qcq() ;
  solution_hom_deux.set_etat_qcq() ;
  resultat.annule_hard() ;

  // Tbls for the boundary condition
  double* bc1 = &par.get_double_mod(1) ;
  double* bc2 = &par.get_double_mod(2) ;
  Tbl* tbc3 = &par.get_tbl_mod(1) ;
  
  for (int l=0 ; l<nz ; l++) {
    solution_part.t[l]->annule_hard() ;
    solution_hom_un.t[l]->annule_hard() ;
    solution_hom_deux.t[l]->annule_hard() ;
  }  
  
  //---------------
  //--  NUCLEUS ---
  //---------------
  int lz = 0 ;
  nr = source.get_mg()->get_nr(lz) ;
  so = new Tbl(nr) ;
  
  alpha = mapping.get_alpha()[lz] ;
  
  for (int k=0 ; k<np+1 ; k++) {
      for (int j=0 ; j<nt ; j++) {
      // quantic numbers and spectral bases
      base.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
      l_quant += dl ;
      if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_quant >=l_min) )
      {
          //Calculation of the coefficients of the operator
          par.get_tbl_mod().set(4,lz) = 2*par.get_tbl_mod()(2,lz) ;
          par.get_tbl_mod().set(5,lz) = 2*par.get_tbl_mod()(3,lz) ;
          par.get_tbl_mod().set(6,lz) = 2*par.get_tbl_mod()(1,lz) ;
          par.get_tbl_mod().set(7,lz) = 
          -l_quant*(l_quant+1)*par.get_tbl_mod()(3,lz) ;
          par.get_tbl_mod().set(8,lz) = 
          -l_quant*(l_quant+1)*par.get_tbl_mod()(2,lz) ;
          par.get_tbl_mod().set(9,lz) = 
          -l_quant*(l_quant+1)*par.get_tbl_mod()(1,lz) ;
      
          Matrice operateur(nr,nr) ;
          
          get_operateur_dal(par, lz, base_r, type_dal, operateur) ;
          
          // Getting the particular solution
          so->set_etat_qcq() ;
          for (int i=0 ; i<nr ; i++)
          so->set(i) = source(lz, k, j, i) ;
          if ((type_dal == ORDRE1_LARGE) || (type_dal == O2DEGE_LARGE)
          || (type_dal == O2NOND_LARGE))
          so->set(nr-1) = 0 ;
          sol_part = new Tbl(dal_inverse(base_r, type_dal, operateur, 
                         *so, true)) ;
          
          // Getting the homogeneous solution
          sol_hom = new Tbl(dal_inverse(base_r, type_dal, operateur, 
                        *so, false)) ;
          
          // Putting to Mtbl_cf
          for (int i=0 ; i<nr ; i++) {
          solution_part.set(lz, k, j, i) = (*sol_part)(i) ;
          solution_hom_un.set(lz, k, j, i) = (*sol_hom)(i) ;
          solution_hom_deux.set(lz, k, j, i) = 0. ; 
          }
      
          // If only one zone, the BC is set
          if (nz0 == 1) {
          
          int base_pipo = 0 ;
          double part, dpart, hom, dhom;
          Tbl der_part(3,1,nr) ;
          der_part.set_etat_qcq() ;
          for (int i=0; i<nr; i++) 
              der_part.set(0,0,i) = (*sol_part)(i) ;
          Tbl der_hom(3,1,nr) ;
          der_hom.set_etat_qcq() ;
          for (int i=0; i<nr; i++) 
              der_hom.set(0,0,i) = (*sol_hom)(i) ;
          
          if (base_r == R_CHEBP) {
              som_r_chebp(sol_part->t, nr, 1, 1, 1., &part) ;
              _dsdx_r_chebp(&der_part, base_pipo) ;
              som_r_chebi(der_part.t, nr, 1, 1, 1., &dpart) ;
              som_r_chebp(sol_hom->t, nr, 1, 1, 1., &hom) ;
              _dsdx_r_chebp(&der_hom, base_pipo) ;
              som_r_chebi(der_hom.t, nr, 1, 1, 1., &dhom) ;
          }
          else {
              som_r_chebi(sol_part->t, nr, 1, 1, 1., &part) ;
              _dsdx_r_chebi(&der_part, base_pipo) ;
              som_r_chebp(der_part.t, nr, 1, 1, 1., &dpart) ;
              som_r_chebi(sol_hom->t, nr, 1, 1, 1., &hom) ;
              _dsdx_r_chebi(&der_hom, base_pipo) ;
              som_r_chebp(der_hom.t, nr, 1, 1, 1., &dhom) ;
          }
        
          part = part*(*bc1) + dpart*(*bc2)/alpha ;
          hom = hom*(*bc1) + dhom*(*bc2)/alpha ;
          double lambda = ((*tbc3)(k,j) - part) / hom ;
          for (int i=0 ; i<nr ; i++)
              resultat.set(lz, k, j, i) = 
              solution_part(lz, k, j, i)
              +lambda*solution_hom_un(lz, k, j, i) ; 
          }
          
          delete sol_hom ;
          delete sol_part ;
      } // nullite_plm
      } // theta loop
  } // phi loop  
  delete so ;

  //---------------------
  //--      SHELLS     --
  //---------------------
  for (lz=1 ; lz<nz0 ; lz++) {
    nr = source.get_mg()->get_nr(lz) ;
    so = new Tbl(nr) ;
    alpha = mapping.get_alpha()[lz] ;
    beta = mapping.get_beta()[lz] ;
    
    for (int k=0 ; k<np+1 ; k++)
    for (int j=0 ; j<nt ; j++) {
        // quantic numbers and spectral bases
        base.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
        l_quant += dl ;
        if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_quant >=l_min) )
        {
        //Calculation of the coefficients of the operator
        par.get_tbl_mod().set(4,lz) = 2*par.get_tbl_mod()(2,lz) ;
        par.get_tbl_mod().set(5,lz) = 2*par.get_tbl_mod()(3,lz) ;
        par.get_tbl_mod().set(6,lz) = 2*par.get_tbl_mod()(1,lz) ;
        par.get_tbl_mod().set(7,lz) = 
            -l_quant*(l_quant+1)*par.get_tbl_mod()(3,lz) ;
        par.get_tbl_mod().set(8,lz) = 
            -l_quant*(l_quant+1)*par.get_tbl_mod()(2,lz) ;
        par.get_tbl_mod().set(9,lz) = 
            -l_quant*(l_quant+1)*par.get_tbl_mod()(1,lz) ;
        
        Matrice operateur(nr,nr) ;
        
        get_operateur_dal(par, lz, base_r, type_dal, operateur) ;
        
        // Calcul DES DEUX SH
        so->set_etat_qcq() ;
        for (int i=0; i<nr; i++) so->set(i) = 0. ;
        so->set(nr-2) = 1. ;
        sol_hom = new Tbl(dal_inverse(base_r, type_dal, operateur, *so,
                          false)) ;
        so->set(nr-2) = 0. ;
        so->set(nr-1) = 1. ;
        sol_hom2 = new Tbl(dal_inverse(base_r, type_dal, operateur, *so,
                           false)) ;
        
        // Calcul de la SP
        double *tmp = new double[nr] ;
        for (int i=0 ; i<nr ; i++)
            tmp[i] = source(lz, k, j, i) ;
        if ((type_dal == O2DEGE_SMALL) || (type_dal == O2DEGE_LARGE)) {
            for (int i=0; i<nr; i++) so->set(i) = beta*tmp[i] ;
            multx_1d(nr, &tmp, R_CHEB) ;
            for (int i=0; i<nr; i++) so->set(i) += alpha*tmp[i] ;
        }
        else {
            for (int i=0; i<nr; i++) so->set(i) = beta*beta*tmp[i] ;
            multx_1d(nr, &tmp, R_CHEB) ;
            for (int i=0; i<nr; i++) so->set(i) += 2*alpha*beta*tmp[i] ;
            multx_1d(nr, &tmp, R_CHEB) ;
            for (int i=0; i<nr; i++) so->set(i) += alpha*alpha*tmp[i] ;
        }
        so->set(nr-2) = 0. ;
        so->set(nr-1) = 0. ;
        
        sol_part = new Tbl (dal_inverse(base_r, type_dal, operateur, 
                        *so, true)) ;       
        // Rangement
        for (int i=0 ; i<nr ; i++) {
            solution_part.set(lz, k, j, i) = (*sol_part)(i) ;
            solution_hom_un.set(lz, k, j, i) = (*sol_hom)(i) ;
            solution_hom_deux.set(lz, k, j, i) = (*sol_hom2)(i) ;
        }
        
        delete [] tmp ;
        delete sol_hom ;
        delete sol_hom2 ;
        delete sol_part ;
        }
    } // theta loop
    delete so ;
  } // domain loop
  if (nz0 > 1) {
    //--------------------------------------------------------------------
    //
    //     Combinations of particular and homogeneous solutions
    //         to verify continuity and boundary conditions
    //
    //--------------------------------------------------------------------
    int taille = 2*nz0 - 1 ; 
    Tbl deuz(taille) ;
    deuz.set_etat_qcq() ;
    Matrice systeme(taille,taille) ;
    systeme.set_etat_qcq() ;
    int sup = 2;
    int inf = (nz0>2) ? 2 : 1 ;
    for (int k=0; k<np+1; k++) {
      for (int j=0; j<nt; j++) {
      // To get the r basis in the nucleus
      base.give_quant_numbers(0, k, j, m_quant, l_quant, base_r) ;
      if ( (nullite_plm(j, nt, k, np, base)) && (l_quant + dl >= l_min) ) {
          assert ((base_r == R_CHEBP)||(base_r == R_CHEBI)) ;
          int parite = (base_r == R_CHEBP) ? 0 : 1 ;
          int l, c ; 
          double xx = 0.;
          for (l=0; l<taille; l++) 
          for (c=0; c<taille; c++) systeme.set(l,c) = xx ;
          for (l=0; l<taille; l++) deuz.set(l) = xx ;
      
          //---------
          // Nucleus
          //---------
          nr = source.get_mg()->get_nr(0) ;
          alpha = mapping.get_alpha()[0] ;
          l=0 ; c=0 ;
          for (int i=0; i<nr; i++) 
          systeme.set(l,c) += solution_hom_un(0, k, j, i) ;
          for (int i=0; i<nr; i++) deuz.set(l) -= solution_part(0, k, j, i) ;
          
          l++ ;
          xx = 0. ;
          for (int i=0; i<nr; i++)
          xx +=(2*i+parite)*(2*i+parite)
              *solution_hom_un(0, k, j, i) ;
          systeme.set(l,c) += xx/alpha ;
          xx = 0. ; 
          for (int i=0; i<nr; i++) xx -= (2*i+parite)*
                       (2*i+parite)*solution_part(0, k, j, i) ;
          deuz.set(l) += xx/alpha ;
      
          //----------
          //  Shells
          //----------
          for (lz=1; lz<nz0; lz++) {
          nr = source.get_mg()->get_nr(lz) ;
          alpha = mapping.get_alpha()[lz] ;
          l-- ; 
          c = l+1 ;
          for (int i=0; i<nr; i++) 
              if (i%2 == 0)
              systeme.set(l,c) -= solution_hom_un(lz, k, j, i) ;
              else
              systeme.set(l,c) += solution_hom_un(lz, k, j, i) ;
          c++ ;
          for (int i=0; i<nr; i++) 
              if (i%2 == 0)
              systeme.set(l,c) -= solution_hom_deux(lz, k, j, i) ;
              else
              systeme.set(l,c) += solution_hom_deux(lz, k, j, i) ;
          for (int i=0; i<nr; i++) 
              if (i%2 == 0) deuz.set(l) += solution_part(lz, k, j, i) ;
              else deuz.set(l) -= solution_part(lz, k, j, i) ;
          
          l++ ; c-- ;
          xx = 0. ;
          for (int i=0; i<nr; i++) 
              if (i%2 == 0)
              xx += i*i*solution_hom_un(lz, k, j, i) ;
              else
              xx -= i*i*solution_hom_un(lz, k, j, i) ;
          systeme.set(l,c) += xx/alpha ;
          c++ ;
          xx = 0. ;
          for (int i=0; i<nr; i++) 
              if (i%2 == 0)
              xx += i*i*solution_hom_deux(lz, k, j, i) ;
              else
              xx -= i*i*solution_hom_deux(lz, k, j, i) ;
          systeme.set(l,c) += xx/alpha ;
          xx = 0. ;
          for (int i=0; i<nr; i++) 
              if (i%2 == 0) xx -= i*i*solution_part(lz, k, j, i) ;
              else xx += i*i*solution_part(lz, k, j, i) ;
          deuz.set(l) += xx/alpha ;
          
          l++ ; c--;
          if (lz == nz0-1) { // Last domain, the outer BC is set
              for (int i=0; i<nr; i++) 
              systeme.set(l,c) +=
                  ((*bc1)+(*bc2)*i*i/alpha)*solution_hom_un(lz, k, j, i) ;
              c++ ;
              for (int i=0; i<nr; i++) 
              systeme.set(l,c) +=
                  ((*bc1)+(*bc2)*i*i/alpha)*solution_hom_deux(lz, k, j, i) ;
              for (int i=0; i<nr; i++) 
              deuz.set(l) -=
                  ((*bc1)+(*bc2)*i*i/alpha)*solution_part(lz, k, j, i) ;
              deuz.set(l) += (*tbc3)(k,j) ;
          }
          else { // At least one more shell
              for (int i=0; i<nr; i++) 
              systeme.set(l,c) += solution_hom_un(lz, k, j, i) ;
              c++ ;
              for (int i=0; i<nr; i++) 
              systeme.set(l,c) += solution_hom_deux(lz, k, j, i) ;
              for (int i=0; i<nr; i++) 
              deuz.set(l) -= solution_part(lz, k, j, i) ;
              l++ ; c-- ;
              xx = 0. ;
              for (int i=0; i<nr; i++) xx += i*i*solution_hom_un(lz, k, j, i) ;
              systeme.set(l,c) += xx/alpha ;
              c++ ;
              xx = 0. ;
              for (int i=0; i<nr; i++) 
              xx += i*i*solution_hom_deux(lz, k, j, i) ;
              systeme.set(l,c) += xx/alpha ;
              xx = 0. ;
              for (int i=0; i<nr; i++) 
              xx -= i*i*solution_part(lz, k, j, i) ;     
              deuz.set(l) += xx/alpha ;
          }
          }

          //--------------------------------------
          //   Solution of the linear system
          //--------------------------------------
      
          systeme.set_band(sup, inf) ;
          systeme.set_lu() ;
          Tbl facteur(systeme.inverse(deuz)) ;
          
          //Linear Combination in the nucleus
          nr = source.get_mg()->get_nr(0) ;
          for (int i=0; i<nr; i++) 
          resultat.set(0, k, j, i) = solution_part(0, k, j, i) 
              + facteur(0)*solution_hom_un(0, k, j, i) ;
          
          //Linear combination in the shells
          for (lz=1; lz<nz0; lz++) {
          nr = source.get_mg()->get_nr(lz) ;
          for (int i=0; i<nr; i++) 
              resultat.set(lz, k, j, i) = solution_part(lz, k, j, i) 
              + facteur(2*lz-1)*solution_hom_un(lz, k, j, i) 
              + facteur(2*lz)*solution_hom_deux(lz, k, j, i) ;
          }
      }        
      } //End of j/theta loop   
    } //End of k/phi loop 
  } //End of case nz0>1
  
  return resultat ;

}

---