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/*
* Test of the resolution of the vector Poisson equation
*
*/
/*
* 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_poisson_vect_C[] = "$Header: /cvsroot/Lorene/Codes/Test/Poisson_vect/test_poisson_vect.C,v 1.3 2014/10/13 08:54:02 j_novak Exp $" ;
/*
* $Id: test_poisson_vect.C,v 1.3 2014/10/13 08:54:02 j_novak Exp $
* $Log: test_poisson_vect.C,v $
* Revision 1.3 2014/10/13 08:54:02 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.2 2006/06/05 09:48:33 j_novak
* Using version 6 of the vector Poisson solver
*
* Revision 1.1 2004/02/22 15:48:49 j_novak
* New code for testing vector Poisson equation.
*
*
* $Header: /cvsroot/Lorene/Codes/Test/Poisson_vect/test_poisson_vect.C,v 1.3 2014/10/13 08:54:02 j_novak Exp $
*
*/
// Lorene headers
#include "metric.h"
#include "tenseur.h"
#include "nbr_spx.h"
#include "utilitaires.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 = 5 ; // Number of collocation points in theta in each domain
int np = 6 ; // 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} ;
assert( nz == 3 ) ;// since the above arrays are described in only 3 domains
Mg3d mgrid(nz, nbr, tipe_r, nbt, symmetry_theta, nbp, symmetry_phi) ;
int nzm1 = nz - 1 ;
// Construction of an affine mapping (Map_af)
// ------------------------------------------
double R = 2.1 ;
// Boundaries of each domains
double r_limits[] = {0., 0.5*R, R, __infinity} ;
Map_af map(mgrid, r_limits) ;
// Construction of flat metrics
// ----------------------------
Metric_flat mets(map, map.get_bvect_spher()) ; // spherical representation
Metric_flat metc(map, map.get_bvect_cart()) ; // Cartesian representation
Scalar xx(map), yy(map), zz(map), rr(map) ;
xx = map.x ;
yy = map.y ;
zz = map.z ;
rr = map.r ;
double lamda = 1. ; //for the vector equation Delta V + lamda grad(div V)
int nn ;
cout << "Enter n : (source decaying like 1/r^n+4, so n>0 is required)"
<< endl ;
cin >> nn ;
Vector theo(map, CON, map.get_bvect_cart()) ;
Vector theo_zec(map, CON, map.get_bvect_cart()) ;
theo.set(1) = xx*rr*rr / (10 * (lamda+1) * pow(R, double(nn+5)))
- double(nn + 5) *xx /
(6 * (lamda + 1) * double(nn+3) * pow(R, double(nn+3))) ;
theo.set(1).annule_domain(nzm1) ;
theo_zec.set(1) = xx / ((lamda+1) * nn * (nn+3) * pow(rr, nn+3))
- (nn+5) * xx / ((lamda+1) * 15*nn * pow(R,double(nn)) * pow(rr,3)) ;
theo_zec.set(1).annule(0,nz-2) ;
theo.set(1) += theo_zec(1) ;
theo.set(1).set_outer_boundary(nz-1, 0.) ;
theo.set(2) = yy*rr*rr / (10 * (lamda+1) * pow(R, double(nn+5)))
- double(nn + 5) *yy / (6 * (lamda + 1) * double(nn+3) * pow(R, double(nn+3))) ;
theo.set(2).annule_domain(nzm1) ;
theo_zec.set(2) = yy / ((lamda+1) * nn * (nn+3) * pow(rr, nn+3))
- (nn+5) * yy / ((lamda+1) * 15*nn * pow(R,double(nn)) * pow(rr,3)) ;
theo_zec.set(2).annule(0,nz-2) ;
theo.set(2) += theo_zec(2) ;
theo.set(2).set_outer_boundary(nz-1, 0.) ;
theo.set(3) = zz*rr*rr / (10 * (lamda+1) * pow(R, double(nn+5)))
- double(nn + 5) *zz / (6 * (lamda + 1) * double(nn+3) * pow(R, double(nn+3))) ;
theo.set(3).annule_domain(nzm1) ;
theo_zec.set(3) = zz / ((lamda+1) * nn * (nn+3) * pow(rr, nn+3))
- (nn+5) * zz / ((lamda+1) * 15*nn * pow(R,double(nn)) * pow(rr,3)) ;
theo_zec.set(3).annule(0,nz-2) ;
theo.set(3) += theo_zec(3) ;
theo.set(3).set_outer_boundary(nz-1, 0.) ;
theo.std_spectral_base() ;
Vector source(map, CON, map.get_bvect_cart()) ;
Vector source_zec(map, CON, map.get_bvect_cart()) ;
source.set(1) = xx / pow(R, double(nn+5)) ;
source.set(1).annule_domain(nzm1) ;
source_zec.set(1) = xx / pow(rr, nn+1) ;
source_zec.set(1).set_dzpuis(4) ;
source_zec.set(1).annule(0, nz-2) ;
source.set(1) += source_zec(1) ;
source.set(1).set_outer_boundary(nz-1, 0.) ;
source.set(2) = yy / pow(R, double(nn+5)) ;
source.set(2).annule_domain(nzm1) ;
source_zec.set(2) = yy / pow(rr, nn+1) ;
source_zec.set(2).set_dzpuis(4) ;
source_zec.set(2).annule(0, nz-2) ;
source.set(2) += source_zec(2) ;
source.set(2).set_outer_boundary(nz-1, 0.) ;
source.set(3) = zz / pow(R, double(nn+5)) ;
source.set(3).annule_domain(nzm1) ;
source_zec.set(3) = zz / pow(rr, nn+1) ;
source_zec.set(3).set_dzpuis(4) ;
source_zec.set(3).annule(0, nz-2) ;
source.set(3) += source_zec(3) ;
source.set(3).set_outer_boundary(nz-1, 0.) ;
source.std_spectral_base() ;
Vector source_s = source ;
source_s.change_triad( map.get_bvect_spher() ) ;
Tenseur source_p(map, 1, CON, map.get_bvect_cart() ) ;
source_p.set_etat_qcq() ;
for (int i=0; i<3; i++) {
source_p.set(i) = Cmp(source(i+1)) ;
}
Tenseur vect_auxi (map, 1, CON, map.get_bvect_cart()) ;
vect_auxi.set_etat_qcq() ;
Tenseur scal_auxi (map) ;
scal_auxi.set_etat_qcq() ;
Tenseur resu_p(source_p.poisson_vect(lamda, vect_auxi, scal_auxi)) ;
Tenseur theo_p(map, 1, CON, map.get_bvect_cart()) ;
theo_p.set_etat_qcq() ;
for (int i=0; i<3; i++) {
theo_p.set(i) = Cmp(theo(i+1)) ;
}
Vector resus = source_s.poisson(lamda, mets,6) ;
Vector resu = resus ;
resu.change_triad(map.get_bvect_cart() ) ;
cout << "Max of relative difference (in cartesian components): " << endl ;
for (int i=1; i<=3; i++) {
cout << "Component " << i << ": " << endl ;
cout << "New version: " << diffrelmax(resu(i), theo(i)) << endl ;
cout << "Grandclement et al.: " <<
diffrelmax(resu_p(i-1), theo_p(i-1)) << endl ;
}
return EXIT_SUCCESS ;
}
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