map_et_poisson_ylm.C

/*
 *  Method of the class Map_et for the (iterative) resolution of the scalar
 *   Poisson equation with a multipole falloff condition at the outer boundary
 *
 *    (see file map.h for documentation).
 *
 */
 
/*
 *   Copyright (c) 2004 Joshua A. Faber
 *
 *   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
 *
 */
 
 
 
/*
 * $Id: map_et_poisson_ylm.C,v 1.3 2016/12/05 16:17:58 j_novak Exp $
 * $Log: map_et_poisson_ylm.C,v $
 * Revision 1.3  2016/12/05 16:17:58  j_novak
 * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
 *
 * Revision 1.2  2014/10/13 08:53:05  j_novak
 * Lorene classes and functions now belong to the namespace Lorene.
 *
 * Revision 1.1  2004/12/30 15:56:42  k_taniguchi
 * *** empty log message ***
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Map/map_et_poisson_ylm.C,v 1.3 2016/12/05 16:17:58 j_novak Exp $
 *
 */
 
// Lorene headers
#include "map.h"
#include "cmp.h"
#include "param.h"
 
//*****************************************************************************
 
namespace Lorene {
 
void Map_et::poisson_ylm(const Cmp& source, Param& par, Cmp& uu, int nylm, double* intvec) const {
 
  assert(source.get_etat() != ETATNONDEF) ; 
    assert(source.get_mp() == this) ;
 
    assert(uu.get_mp() == this) ; 
 
 
    int nz = mg->get_nzone() ; 
 
    //-------------------------------
    // Computation of the prefactor a  ---> Cmp apre
    //-------------------------------
 
    Mtbl unjj = 1 + srdrdt*srdrdt + srstdrdp*srstdrdp ;
 
    Mtbl apre1(*mg) ; 
    apre1.set_etat_qcq() ; 
    for (int l=0; l<nz; l++) {
    *(apre1.t[l]) = alpha[l]*alpha[l] ; 
    }
 
    apre1 = apre1 * dxdr * dxdr * unjj ;
 
 
    Cmp apre(*this) ; 
    apre = apre1 ; 
    
    Tbl amax0 = max(apre1) ;    // maximum values in each domain
 
    // The maximum values of a in each domain are put in a Mtbl
    Mtbl amax1(*mg) ; 
    amax1.set_etat_qcq() ; 
    for (int l=0; l<nz; l++) {
    *(amax1.t[l]) = amax0(l) ; 
    }
 
    Cmp amax(*this) ; 
    amax = amax1 ; 
 
    //-------------------
    //  Initializations 
    //-------------------
    
    int nitermax = par.get_int() ; 
    int& niter = par.get_int_mod() ; 
    double lambda = par.get_double() ; 
    lambda=1.0;
    double unmlambda = 1. - lambda ; 
    double precis = par.get_double(1) ;     
 
    cout <<"relax in map_et:"<<lambda<<" "<<unmlambda<<endl;
    
    Cmp& ssj = par.get_cmp_mod() ; 
    
    Cmp ssjm1 = ssj ; 
    Cmp ssjm2 = ssjm1 ; 
 
    Valeur& vuu = uu.va ; 
 
    Valeur vuujm1(*mg) ;
    if (uu.get_etat() == ETATZERO) {
    vuujm1 = 1 ;    // to take relative differences
    vuujm1.set_base( vuu.base ) ; 
    }
    else{
    vuujm1 = vuu ; 
    }
    
    // Affine mapping for the Laplacian-tilde
 
    Map_af mpaff(*this) ; 
    Param par_nul ; 
 
    cout << "Map_et::poisson : relat. diff. u^J <-> u^{J-1} : " << endl ;
    
//==========================================================================
//==========================================================================
//              Start of iteration 
//==========================================================================
//==========================================================================
 
    Tbl tdiff(nz) ; 
    double diff ; 
    niter = 0 ; 
    
    do {
 
    //====================================================================
    //      Computation of R(u)    (the result is put in uu)
    //====================================================================
 
 
    //-----------------------
    // First operations on uu
    //-----------------------
    
    Valeur duudx = (uu.va).dsdx() ;     // d/dx 
 
    const Valeur& d2uudtdx = duudx.dsdt() ;     // d^2/dxdtheta
 
    const Valeur& std2uudpdx = duudx.stdsdp() ;    // 1/sin(theta) d^2/dxdphi   
 
    //------------------
    // Angular Laplacian 
    //------------------
    
    Valeur sxlapang = uu.va ; 
 
    sxlapang.ylm() ; 
    
    sxlapang = sxlapang.lapang() ;    
    
    sxlapang = sxlapang.sx() ;    //  Lap_ang(uu) /x      in the nucleus
                  //  Lap_ang(uu)         in the shells
                  //  Lap_ang(uu) /(x-1)  in the ZEC
    
    //---------------------------------------------------------------
    //  Computation of 
    // [ 2 /(dRdx) ( A - 1 ) duu/dx + 1/R (B - 1) Lap_ang(uu) ] / x
    //
    // with A = 1/(dRdx) R/(x+beta_l/alpha_l) unjj 
    //      B = [1/(dRdx) R/(x+beta_l/alpha_l)]^2 unjj 
    // 
    //  The result is put in uu (via vuu)
    //---------------------------------------------------------------
 
    Valeur varduudx = duudx ; 
 
    uu.set_etat_qcq() ; 
    
    Base_val sauve_base = varduudx.base ; 
    
    vuu = 2. * dxdr * ( rsxdxdr * unjj - 1.) * varduudx 
        + ( rsxdxdr*rsxdxdr * unjj - 1.) * xsr * sxlapang ; 
 
    vuu.set_base(sauve_base) ; 
 
    vuu = vuu.sx() ; 
 
    //---------------------------------------
    // Computation of  R(u)  
    //
    //  The result is put in uu (via vuu)
    //---------------------------------------
 
 
    sauve_base = vuu.base ; 
 
    vuu =  xsr * vuu 
        + 2. * dxdr * ( sr2drdt * d2uudtdx 
                  + sr2stdrdp * std2uudpdx ) ;
 
    vuu += dxdr * ( lapr_tp + dxdr * ( 
        dxdr* unjj * d2rdx2 
        - 2. * ( sr2drdt * d2rdtdx  + sr2stdrdp * sstd2rdpdx ) ) 
                 ) * duudx ;            
 
    vuu.set_base(sauve_base) ; 
    
    // Since the assignment is performed on vuu (uu.va), the treatment
    //  of uu.dzpuis must be performed by hand:
    
 
    //====================================================================
    //   Computation of the effective source s^J of the ``affine''
    //     Poisson equation 
    //====================================================================
    
    ssj = lambda * ssjm1 + unmlambda * ssjm2 ; 
    
    ssj = ( source + uu + (amax - apre) * ssj ) / amax ; 
 
    (ssj.va).set_base((source.va).base) ; 
    
    //====================================================================
    //   Resolution of the ``affine'' Poisson equation 
    //====================================================================
    
    // *****************************************************************
 
    mpaff.poisson_ylm(ssj, par_nul, uu, nylm, intvec) ; 
 
    // *****************************************************************
 
    tdiff = diffrel(vuu, vuujm1) ; 
 
    diff = max(tdiff) ;
    
 
        cout << "  iter: " << niter << " :  " ; 
    for (int l=0; l<nz; l++) {
        cout << tdiff(l) << "  " ;  
    }
        cout << endl ; 
 
    //=================================
    //  Updates for the next iteration
    //=================================
    
    ssjm2 = ssjm1 ; 
    ssjm1 = ssj ; 
    vuujm1 = vuu ; 
    
    niter++ ; 
    
    }   // End of iteration 
    while ( (diff > precis) && (niter < nitermax) ) ;
    
//==========================================================================
//==========================================================================
//              End of iteration 
//==========================================================================
//==========================================================================
 
   
 
}
 
 
}