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/*
* Test of the resolution of the vector Poisson equation for a given l
*
*/
/*
* Copyright (c) 2004 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 test_vpoisson_l_C[] = "$Header: /cvsroot/Lorene/Codes/Test/Poisson_vect/test_vpoisson_l.C,v 1.7 2014/10/13 08:54:02 j_novak Exp $" ;
/*
* $Id: test_vpoisson_l.C,v 1.7 2014/10/13 08:54:02 j_novak Exp $
* $Log: test_vpoisson_l.C,v $
* Revision 1.7 2014/10/13 08:54:02 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.6 2005/04/06 14:38:41 j_novak
* Added method 6: block inversion with spherical components
*
* Revision 1.5 2004/12/29 12:25:51 j_novak
* non-symmetric grid in phi.
*
* Revision 1.4 2004/07/27 09:40:34 j_novak
* test of method 5.
*
* Revision 1.3 2004/05/07 15:33:24 j_novak
* Treated the case where all components are null.
*
* Revision 1.2 2004/03/26 17:05:24 j_novak
* Added new method n.3 using Tenseur::poisson_vect_oohara
*
* Revision 1.1 2004/03/26 15:35:46 j_novak
* More vector Poisson testing
*
*
* $Header: /cvsroot/Lorene/Codes/Test/Poisson_vect/test_vpoisson_l.C,v 1.7 2014/10/13 08:54:02 j_novak Exp $
*
*/
// Lorene headers
#include "metric.h"
#include "cmp.h"
#include "nbr_spx.h"
#include "utilitaires.h"
#include "graphique.h"
using namespace Lorene ;
int main() {
// Construction of a multi-grid (Mg3d)
// -----------------------------------
const int nz = 3 ; // Number of domains
int nr =33 ; // Number of collocation points in r in each domain
int nt =9 ; // Number of collocation points in theta in each domain
int np = 16 ; // Number of collocation points in phi in each domain
int symmetry_theta = SYM ; // symmetry with respect to the equatorial plane
int symmetry_phi = NONSYM ; // no symmetry in phi
int nbr[] = {nr, nr, nr};
int nbt[] = {nt, nt, nt} ;
int nbp[] = {np, np, np} ;
int tipe_r[] = {RARE, FIN, UNSURR} ;
Mg3d mgrid(nz, nbr, tipe_r, nbt, symmetry_theta, nbp, symmetry_phi) ;
// Construction of an affine mapping (Map_af)
// ------------------------------------------
// Boundaries of each domains
double r_limits[] = {0., 1.1, 2., __infinity} ;
Map_af map(mgrid, r_limits) ;
int nzm1 = nz - 1 ;
// Construction of flat metrics
// ----------------------------
const Metric_flat& mets = map.flat_met_spher() ;
Scalar r(map) ;
r = map.r ;
Scalar xx(map) ;
xx = map.x ;
cout << "Entrer l: " << endl ;
int lq; cin >> lq ;
Scalar pot(map) ;
pot = pow(xx,lq) / (1 + pow(r, 2*lq+2) ) ;
pot.set_outer_boundary(nzm1,0.) ;
pot.std_spectral_base() ;
Vector sol(map, CON, map.get_bvect_cart()) ;
sol.set(1) = pot.dsdy() ;
sol.set(1).dec_dzpuis(2) ;
sol.set(2) = 0 ;
sol.set(3) = 0 ;
sol.change_triad(map.get_bvect_spher()) ;
Vector_divfree sol_df = sol.div_free(mets) ;
Scalar poten = sol.potential(mets) ;
Scalar diff = sol_df.divergence(mets) ;
maxabs(diff, "Divergence de sol_df") ;
double lambda = 1./3. ;
Tensor grad = sol.derive_con(mets) ;
Scalar div = sol.divergence(mets) ;
Vector source = grad.divergence(mets) + lambda * div.derive_con(mets) ;
source.inc_dzpuis() ;
Vector_divfree sou_df = source.div_free(mets) ;
Scalar pot_sou = source.potential(mets) ;
diff = sou_df.divergence(mets) ;
diff.dec_dzpuis() ;
diff.dec_dzpuis(4) ;
maxabs(diff, "Divergence de sou_df") ;
Vector sol_num0 = source.poisson(lambda, 0) ;
Vector sol_num1 = source.poisson(lambda, 1) ;
Vector sol_num2 = source.poisson(lambda, 2) ;
Vector sol_num3 = source.poisson(lambda, 3) ;
Vector sol_num4 = source.poisson(lambda, 4) ;
Vector sol_num5 = source.poisson(lambda, 5) ;
Vector sol_num6 = source.poisson(lambda, 6) ;
cout << endl ;
cout << "==================================================" << endl ;
cout << " --------- Erreur sur la solution --------- " << endl ;
cout << "==================================================" << endl ;
maxabs(sol_num0 - sol, "Methode 0 (Comp. spheriques)") ;
maxabs(sol_num1 - sol, "Methode 1 (Comp. spheriques)") ;
maxabs(sol_num2 - sol, "Methode 2 (Comp. cartesiennes)") ;
maxabs(sol_num3 - sol, "Methode 3 (Comp. cartesiennes)") ;
maxabs(sol_num4 - sol, "Methode 4 (Comp. spheriques)") ;
maxabs(sol_num5 - sol, "Methode 5 (Comp. spheriques)") ;
maxabs(sol_num6 - sol, "Methode 6 (Comp. spheriques)") ;
return EXIT_SUCCESS ;
}
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