sym_tensor_trans_pde.C

/*
 *  Functions to solve various PDEs for a divergence-free symmetric tensor.
 *
 *    (see file sym_tensor.h for documentation).
 *
 */

/*
 *   Copyright (c) 2005-2006  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 sym_tensor_trans_pde_C[] = "$Header: /cvsroot/Lorene/C++/Source/Tensor/sym_tensor_trans_pde.C,v 1.14 2010/10/11 10:38:34 j_novak Exp $" ;

/*
 * $Id: sym_tensor_trans_pde.C,v 1.14 2010/10/11 10:38:34 j_novak Exp $
 * $Log: sym_tensor_trans_pde.C,v $
 * Revision 1.14  2010/10/11 10:38:34  j_novak
 * *** empty log message ***
 *
 * Revision 1.13  2010/10/11 10:23:03  j_novak
 * Removed methods Sym_tensor_trans::solve_hrr() and Sym_tensor_trans::set_WX_det_one(), as they are no longer relevant.
 *
 * Revision 1.12  2006/09/05 15:38:45  j_novak
 * The fuctions sol_Dirac... are in a seperate file, with new parameters to
 * control the boundary conditions.
 *
 * Revision 1.11  2006/08/31 12:13:22  j_novak
 * Added an argument of type Param to Sym_tensor_trans::sol_Dirac_A().
 *
 * Revision 1.10  2006/06/28 07:48:26  j_novak
 * Better treatment of some null cases.
 *
 * Revision 1.9  2006/06/21 15:42:47  j_novak
 * Minor changes.
 *
 * Revision 1.8  2006/06/20 12:07:15  j_novak
 * Improved execution speed for sol_Dirac_tildeB...
 *
 * Revision 1.7  2006/06/14 10:04:21  j_novak
 * New methods sol_Dirac_l01, set_AtB_det_one and set_AtB_trace_zero.
 *
 * Revision 1.6  2006/06/13 13:30:12  j_novak
 * New members sol_Dirac_A and sol_Dirac_tildeB (see documentation).
 *
 * Revision 1.5  2006/06/12 13:37:23  j_novak
 * Added bounds in l (multipolar momentum) for Sym_tensor_trans::solve_hrr.
 *
 * Revision 1.4  2005/11/28 14:45:17  j_novak
 * Improved solution of the Poisson tensor equation in the case of a transverse
 * tensor.
 *
 * Revision 1.3  2005/11/24 14:07:54  j_novak
 * Use of Matrice::annule_hard()
 *
 * Revision 1.2  2005/11/24 09:24:25  j_novak
 * Corrected some missing references.
 *
 * Revision 1.1  2005/09/16 13:58:11  j_novak
 * New Poisson solver for a Sym_tensor_trans.
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Tensor/sym_tensor_trans_pde.C,v 1.14 2010/10/11 10:38:34 j_novak Exp $
 *
 */

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

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

Sym_tensor_trans Sym_tensor_trans::poisson(const Scalar* h_guess) const {

    // All this has a meaning only for spherical components...
    assert(dynamic_cast<const Base_vect_spher*>(triad) != 0x0) ; 
    //## ... and affine mapping, for the moment!
    const Map_af* mpaff = dynamic_cast<const Map_af*>(mp) ;
    assert( mpaff!= 0x0) ;
    Sym_tensor_trans resu(*mp, *triad, *met_div) ;

    const Mg3d& gri = *mp->get_mg() ;
    int np = gri.get_np(0) ;
    int nt = gri.get_nt(0) ;
    assert (nt > 4) ;
    if (np == 1) {
    int nz = gri.get_nzone() ;
    double* bornes = new double[nz+1] ;
    const double* alp = mpaff->get_alpha() ;
    const double* bet = mpaff->get_beta() ; 
    for (int lz=0; lz<nz; lz++) {
        assert (gri.get_np(lz) == np) ;
        assert (gri.get_nt(lz) == nt) ;
        switch (gri.get_type_r(lz)) {
        case RARE: {
            bornes[lz] = bet[lz] ;
            break ;
        }
        case FIN: {
            bornes[lz] = bet[lz] - alp[lz] ;
            break ;
        }
        case UNSURR: {
            bornes[lz] = double(1) / ( bet[lz] - alp[lz] ) ;
            break ;
        }
        default: {
            cout << "Sym_tensor_trans::poisson() : problem with the grid!" 
             << endl ;
            abort() ;
            break ;
        }
        }
    }
    if (gri.get_type_r(nz-1) == UNSURR) 
        bornes[nz] = 1./(alp[nz-1] + bet[nz-1]) ;
    else
        bornes[nz] = alp[nz-1] + bet[nz-1] ;
    
    const Mg3d& gr2 = *gri.get_non_axi() ;
    Map_af mp2(gr2, bornes) ;
    int np2 = ( np > 3 ? np : 4 ) ;
    
    Sym_tensor sou_cart(mp2, CON, mp2.get_bvect_spher()) ;
    for (int l=1; l<=3; l++)
        for (int c=l; c<=3; c++) {
        switch (this->operator()(l,c).get_etat() ) {
            case ETATZERO: {
            sou_cart.set(l,c).set_etat_zero() ;
            break ;
            }
            case ETATUN: {
            sou_cart.set(l,c).set_etat_one() ;
            break ;
            }
            case ETATQCQ : {
            sou_cart.set(l,c).allocate_all() ;
            for (int lz=0; lz<nz; lz++)             
                for (int k=0; k<np2; k++)
                for (int j=0; j<nt; j++)
                    for(int i=0; i<gr2.get_nr(lz); i++)
                    sou_cart.set(l,c).set_grid_point(lz, k, j, i)
                   = this->operator()(l,c).val_grid_point(lz, 0, j, i) ;
            break ;
            }
            default: {
            cout << 
                "Sym_tensor_trans::poisson() : source in undefined state!" 
                 << endl ;
            abort() ;
            break ; 
            }
        }
        sou_cart.set(l,c).set_dzpuis(this->operator()(l,c).get_dzpuis()) ;
        }
    sou_cart.std_spectral_base() ;
    sou_cart.change_triad(mp2.get_bvect_cart()) ;
    Sym_tensor res_cart(mp2, CON, mp2.get_bvect_cart()) ;
    for (int i=1; i<=3; i++)
        for(int j=i; j<=3; j++) 
        res_cart.set(i,j) = sou_cart(i,j).poisson() ;
    res_cart.change_triad(mp2.get_bvect_spher()) ;
    Scalar res_A(*mp) ; Scalar big_A = res_cart.compute_A() ;
    Scalar res_B(*mp) ; Scalar big_B = res_cart.compute_tilde_B_tt() ;

    switch (big_A.get_etat() ) {
        case ETATZERO: {
        res_A.set_etat_zero() ;
        break ;
        }
        case ETATUN : {
        res_A.set_etat_one() ;
        break ;
        }
        case ETATQCQ : {
        res_A.allocate_all() ;
        for (int lz=0; lz<nz; lz++)             
            for (int k=0; k<np; k++)
            for (int j=0; j<nt; j++)
                for(int i=0; i<gri.get_nr(lz); i++)
                res_A.set_grid_point(lz, k, j, i)
                    = big_A.val_grid_point(lz, k, j, i) ;
        break ;
        }
        default: {
        cout << 
            "Sym_tensor_trans::poisson() : res_A in undefined state!" 
             << endl ;
        abort() ;
        break ; 
        }
    }
    res_A.set_spectral_base(big_A.get_spectral_base()) ;
    int dzA = big_A.get_dzpuis() ;
    res_A.set_dzpuis(dzA) ;

    switch (big_B.get_etat() ) {
        case ETATZERO: {
        res_B.set_etat_zero() ;
        break ;
        }
        case ETATUN : {
        res_B.set_etat_one() ;
        break ;
        }
        case ETATQCQ : {
        res_B.allocate_all() ;
        for (int lz=0; lz<nz; lz++)             
            for (int k=0; k<np; k++)
            for (int j=0; j<nt; j++)
                for(int i=0; i<gri.get_nr(lz); i++)
                res_B.set_grid_point(lz, k, j, i)
                    = big_B.val_grid_point(lz, k, j, i) ;
        break ;
        }
        default: {
        cout << 
            "Sym_tensor_trans::poisson() : res_B in undefined state!" 
             << endl ;
        abort() ;
        break ; 
        }
    }
    res_B.set_spectral_base(big_B.get_spectral_base()) ;
    int dzB = big_B.get_dzpuis() ;
    res_B.set_dzpuis(dzB) ;
    
    resu.set_AtBtt_det_one(res_A, res_B, h_guess) ;
    
    delete [] bornes ;
    }
    else {
    assert (np >=4) ;
    Sym_tensor_trans sou_cart = *this ;
    sou_cart.change_triad(mp->get_bvect_cart()) ;
    
    Sym_tensor res_cart(*mp, CON, mp->get_bvect_cart()) ;
    for (int i=1; i<=3; i++)
        for(int j=i; j<=3; j++) 
        res_cart.set(i,j) = sou_cart(i,j).poisson() ;

    res_cart.change_triad(*triad) ;
    
    resu.set_AtBtt_det_one(res_cart.compute_A(), res_cart.compute_tilde_B_tt(), h_guess) ;
    
    }
#ifndef NDEBUG
    Vector dive = resu.divergence(*met_div) ;
    dive.dec_dzpuis(2) ;
    maxabs(dive, "Sym_tensor_trans::poisson : divergence of the solution") ;
#endif    
    return resu ;   
}

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