scalar_sol_div.C

/*
 *  Resolution of the divergence ODE: df/df + n*f/r = source (source must have dzpuis =2)
 *
 *    (see file scalar.h for documentation).
 *
 */

/*
 *   Copyright (c) 2005  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 version 2
 *   as published by the Free Software Foundation.
 *
 *   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 scalar_sol_div_C[] = "$Header: /cvsroot/Lorene/C++/Source/Tensor/Scalar/scalar_sol_div.C,v 1.3 2005/09/16 14:33:00 j_novak Exp $" ;

/*
 * $Id: scalar_sol_div.C,v 1.3 2005/09/16 14:33:00 j_novak Exp $
 * $Log: scalar_sol_div.C,v $
 * Revision 1.3  2005/09/16 14:33:00  j_novak
 * Added #include <math.h>.
 *
 * Revision 1.2  2005/09/16 12:49:52  j_novak
 * The case with dzpuis=1 is added.
 *
 * Revision 1.1  2005/06/08 12:35:22  j_novak
 * New method for solving divergence-like ODEs.
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Tensor/Scalar/scalar_sol_div.C,v 1.3 2005/09/16 14:33:00 j_novak Exp $
 *
 */

// C headers
#include<assert.h>
#include<math.h>

//Lorene headers
#include "tensor.h"
#include "diff.h"
#include "proto.h"

// Local prototypes 
void _sx_r_chebp(Tbl* , int& ) ;
void _sx_r_chebi(Tbl* , int& ) ;


Scalar Scalar::sol_divergence(int n_factor) const {

    assert(etat != ETATNONDEF) ;
    const Map_af* mpaff = dynamic_cast<const Map_af*>(mp) ;
    assert( mpaff != 0x0) ;

    Scalar result(*mp) ;

    if ( etat == ETATZERO )
    result.set_etat_zero() ;
    else {                                             //source not zero
    Base_val base_resu = get_spectral_base() ;
    base_resu.mult_x() ;
    const Mg3d* mg = mp->get_mg() ;
    result.set_etat_qcq() ; result.set_spectral_base(base_resu) ;
    result.set_spectral_va().set_etat_cf_qcq() ;
    Valeur sigma(va) ;
    sigma.ylm_i() ;                               // work on Fourier basis
    const Mtbl_cf& source = *sigma.c_cf ;

    // Checks on the type of domains
    int nz = mg->get_nzone() ;
    bool ced = (mg->get_type_r(nz-1) == UNSURR ) ;
    assert ( (!ced) || (check_dzpuis(2)) || (check_dzpuis(1)) ) ;
    assert (mg->get_type_r(0) == RARE) ;
    int nt = mg->get_nt(0) ;
    int np = mg->get_np(0) ;
#ifndef NDEBUG
    for (int lz = 0; lz<nz; lz++)
        assert( (mg->get_nt(lz) == nt) && (mg->get_np(lz) == np) ) ;
#endif
    int nr, base_r,l_quant, m_quant;
    Tbl *so ;
    Tbl *s_hom ;
    Tbl *s_part ;
  
    // Working objects and initialization
    Mtbl_cf sol_part(mg, base_resu) ;
    Mtbl_cf sol_hom(mg, base_resu) ;
    Mtbl_cf& resu = *result.set_spectral_va().c_cf ;
    sol_part.annule_hard();
    sol_hom.annule_hard() ;
    resu.annule_hard() ;

    //---------------
    //--  NUCLEUS ---
    //---------------
    int lz = 0 ;  
    nr = mg->get_nr(lz) ;

        int dege = 1 ; // the operator is degenerate
    int nr0 = nr - dege ;
    Tbl vect1(3, 1, nr) ; 
    Tbl vect2(3, 1, nr) ;
    int base_pipo = 0 ;
    double alpha = mpaff->get_alpha()[lz] ;
    double beta =  0. ;
    Matrice ope_even(nr0, nr0) ; //when the *result* is decomposed on R_CHEBP
    ope_even.set_etat_qcq() ;
    for (int i=dege; i<nr; i++) {
        vect1.annule_hard() ;
        vect2.annule_hard() ;
        vect1.set(0,0,i) = 1. ; vect2.set(0,0,i) = 1. ;
        _dsdx_r_chebp(&vect1, base_pipo) ;
        _sx_r_chebp(&vect2, base_pipo) ;
        for (int j=0; j<nr0; j++)
        ope_even.set(j,i-dege) = (vect1(0,0,j) + n_factor*vect2(0,0,j)) / alpha ;
    }
    ope_even.set_lu() ;
    Matrice ope_odd(nr0, nr0) ; //when the *result* is decomposed on R_CHEBI
    ope_odd.set_etat_qcq() ;
    for (int i=0; i<nr0; i++) {
        vect1.annule_hard() ;
        vect2.annule_hard() ;
        vect1.set(0,0,i) = 1. ; vect2.set(0,0,i) = 1. ;
        _dsdx_r_chebi(&vect1, base_pipo) ;
        _sx_r_chebi(&vect2, base_pipo) ;
        for (int j=0; j<nr0; j++)
        ope_odd.set(j,i) = (vect1(0,0,j) + n_factor*vect2(0,0,j)) / alpha ;
    }
    ope_odd.set_lu() ;
  
    for (int k=0 ; k<np+1 ; k++) 
        for (int j=0 ; j<nt ; j++) {
        // to get the spectral base
        base_resu.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
        assert ( (base_r == R_CHEBP) || (base_r == R_CHEBI) ) ;
        const Matrice& operateur = (( base_r == R_CHEBP ) ? 
                        ope_even : ope_odd ) ;
        // particular solution 
        so = new Tbl(nr0) ;
        so->set_etat_qcq() ;
        for (int i=0 ; i<nr0 ; i++)
            so->set(i) = source(lz, k, j, i) ;

        s_part = new Tbl(operateur.inverse(*so)) ;
        
        // Putting to Mtbl_cf     
        double somme = 0 ;
        for (int i=0 ; i<nr0 ; i++) {
            if (base_r == R_CHEBP) {
            resu.set(lz, k, j, i+dege) = (*s_part)(i) ;
            somme += ((i+dege)%2 == 0 ? 1 : -1)*(*s_part)(i) ;
            }
            else 
            resu.set(lz,k,j,i) = (*s_part)(i) ;
        }
        if (base_r == R_CHEBI) 
            for (int i=nr0; i<nr; i++) 
            resu.set(lz,k,j,i) = 0 ; 
        if (base_r == R_CHEBP) //result must vanish at r=0
            resu.set(lz, k, j, 0) -= somme ;

        delete so ;
        delete s_part ;
        
        }
    
    //---------------------
    //--      SHELLS     --
    //---------------------
    int nz0 = (ced ? nz - 1 : nz) ;
    for (lz=1 ; lz<nz0 ; lz++) {
        nr = mg->get_nr(lz) ;    
        alpha = mpaff->get_alpha()[lz] ;
        beta =  mpaff->get_beta()[lz];
        double ech = beta / alpha ;
        Diff_id id(R_CHEB, nr) ; const Matrice& mid = id.get_matrice() ; 
        Diff_xdsdx xd(R_CHEB, nr) ; const Matrice& mxd = xd.get_matrice() ;
        Diff_dsdx dx(R_CHEB, nr) ; const Matrice& mdx = dx.get_matrice() ;
        Matrice operateur = mxd + ech*mdx + n_factor*mid ;
        operateur.set_lu() ;
        // homogeneous solution
        s_hom = new Tbl(solh(nr, n_factor-1, ech, R_CHEB)) ;
        
        for (int k=0 ; k<np+1 ; k++)
        for (int j=0 ; j<nt ; j++) {
            // to get the spectral base
            base_resu.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
            assert (base_r == R_CHEB) ;
            
            so = new Tbl(nr) ;
            so->set_etat_qcq() ;
            // particular solution
            Tbl tmp(nr) ;
            tmp.set_etat_qcq() ;
            for (int i=0 ; i<nr ; i++)
            tmp.set(i) = source(lz, k, j, i) ;
            for (int i=0; i<nr; i++) so->set(i) = beta*tmp(i) ;
            multx_1d(nr, &tmp.t, R_CHEB) ;
            for (int i=0; i<nr; i++) so->set(i) += alpha*tmp(i)  ;
            
            s_part = new Tbl (operateur.inverse(*so)) ;
            
            // cleaning things...
            for (int i=0 ; i<nr ; i++) {
            sol_part.set(lz, k, j, i) = (*s_part)(i) ;
            sol_hom.set(lz, k, j, i) = (*s_hom)(1,i) ;
            }
            
            delete so ;
            delete s_part ;
        }
        delete s_hom ;
    }
    if (ced) {
    //---------------
    //--  CED   -----
    //---------------
        int dzp = ( check_dzpuis(2) ? 2 : 1) ;
        nr = source.get_mg()->get_nr(nz-1) ;
        alpha = mpaff->get_alpha()[nz-1] ;
        beta = mpaff->get_beta()[nz-1] ;
        dege = dzp  ;
        nr0 = nr - dege ;
        Diff_dsdx dx(R_CHEBU, nr) ; const Matrice& mdx = dx.get_matrice() ;
        Diff_sx sx(R_CHEBU, nr) ; const Matrice& msx = sx.get_matrice() ;
        Diff_xdsdx xdx(R_CHEBU, nr) ; const Matrice& mxdx = xdx.get_matrice() ;
        Diff_id id(R_CHEBU, nr) ; const Matrice& mid = id.get_matrice() ;
        Matrice operateur(nr0, nr0) ;
        operateur.set_etat_qcq() ;
        if (dzp == 2)
        for (int lin=0; lin<nr0; lin++) 
            for (int col=dege; col<nr; col++)
            operateur.set(lin,col-dege) = (-mdx(lin,col) 
                    + n_factor*msx(lin, col)) / alpha ;
        else {
        for (int lin=0; lin<nr0; lin++) {
            for (int col=dege; col<nr; col++)
            operateur.set(lin,col-dege) = (-mxdx(lin,col) 
                    + n_factor*mid(lin, col)) ;
        }
        }
        operateur.set_lu() ;
        // homogeneous solution
        s_hom = new Tbl(solh(nr, n_factor-1, 0., R_CHEBU)) ;
        for (int k=0 ; k<np+1 ; k++)
        for (int j=0 ; j<nt ; j++) {
            base_resu.give_quant_numbers(lz, k, j, m_quant, l_quant, base_r) ;
            assert(base_r == R_CHEBU) ;     
            
            // particular solution
            so = new Tbl(nr0) ;
            so->set_etat_qcq() ;
            for (int i=0 ; i<nr0 ; i++)
            so->set(i) = source(nz-1, k, j, i) ;
            s_part = new Tbl(operateur.inverse(*so)) ;

            // cleaning
            double somme = 0 ;
            for (int i=0 ; i<nr0 ; i++) {
            sol_part.set(nz-1, k, j, i+dege) = (*s_part)(i) ;
            somme += (*s_part)(i) ;
            sol_hom.set(nz-1, k, j, i) = (*s_hom)(i) ;
            }
            for (int i=nr0; i<nr; i++)
            sol_hom.set(nz-1, k, j, i) = (*s_hom)(i) ;
            //result must vanish at infinity
            sol_part.set(nz-1, k, j, 0) = -somme ; 
            delete so ;
            delete s_part ;
        }
        delete s_hom ;
    }
    
    //-------------------------
    //-- matching solutions ---
    //-------------------------
    if (nz > 1) { 
        Tbl echelles(nz-1) ;
        echelles.set_etat_qcq() ;
        for (lz=1; lz<nz; lz++) 
        echelles.set(lz-1) 
            = pow ( (mpaff->get_beta()[lz]/mpaff->get_alpha()[lz] -1), 
                n_factor) ;
        if (ced) echelles.set(nz-2) = 1./pow(-2., n_factor) ;
        
        for (int k=0 ; k<np+1 ; k++)
        for (int j=0 ; j<nt ; j++) {
            for (lz=1; lz<nz; lz++) {
            double val1 = 0 ;
            double valm1 = 0 ;
            double valhom1 = 0 ;
            int nr_prec = mg->get_nr(lz-1) ;
            nr = mg->get_nr(lz) ;
            for (int i=0; i<nr_prec; i++)
                val1 += resu(lz-1, k, j, i) ;
            for (int i=0; i<nr; i++) {
                valm1 += ( i%2 == 0 ? 1 : -1)*sol_part(lz, k, j, i) ;
                valhom1 += ( i%2 == 0 ? 1 : -1)*sol_hom(lz, k, j, i) ;
            }
            double lambda = (val1 - valm1) * echelles(lz-1) ;
            for (int i=0; i<nr; i++)
                resu.set(lz, k, j, i) = sol_part(lz, k, j, i) 
                + lambda*sol_hom(lz, k, j, i) ;

            }
        }
    }
    }
    return result ;
}

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