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/*
* Code for testing the divergence-free vector Poisson equation.
*
*/
/*
* Copyright (c) 2003 Eric Gourgoulhon & 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_vdf_poisson_C[] = "$Header: /cvsroot/Lorene/Codes/Test/Poisson_vect/test_vdf_poisson.C,v 1.7 2014/10/13 08:54:02 j_novak Exp $" ;
/*
* $Id: test_vdf_poisson.C,v 1.7 2014/10/13 08:54:02 j_novak Exp $
* $Log: test_vdf_poisson.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 2014/10/06 15:12:55 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.5 2003/10/29 13:16:11 e_gourgoulhon
* Change of method name: Scalar::laplacien --> Scalar::laplacian.
*
* Revision 1.4 2003/10/29 11:06:11 e_gourgoulhon
* inc2_dzpuis() replaced by inc_dzpuis(2).
*
* Revision 1.3 2003/10/21 13:59:36 e_gourgoulhon
* new version
*
* Revision 1.2 2003/10/20 19:46:41 e_gourgoulhon
* First successful version.
*
* Revision 1.1 2003/10/20 14:46:22 e_gourgoulhon
* First version
*
*
* $Header: /cvsroot/Lorene/Codes/Test/Poisson_vect/test_vdf_poisson.C,v 1.7 2014/10/13 08:54:02 j_novak Exp $
*
*/
// C++ headers
#include "headcpp.h"
// C headers
#include <cstdlib>
// Lorene headers
#include "metric.h"
#include "nbr_spx.h"
#include "utilitaires.h"
using namespace Lorene ;
int main() {
// Construction of a multi-grid (Mg3d)
// -----------------------------------
int nz = 3 ; // Number of domains
int nzm1 = nz - 1 ;
int nr = 17 ; // Number of collocation points in r in each domain
int nt = 17; // Number of collocation points in theta in each domain
int np = 12 ; // 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
bool compact = true ; // external domain is compactified
Mg3d mgrid(nz, nr, nt, np, symmetry_theta, symmetry_phi, compact) ;
// Construction of an affine mapping (Map_af)
// ------------------------------------------
// Boundaries of each domains
double r_limits[] = {0., 0.5, 1., __infinity} ;
assert( nz == 3 ) ; // since the above array described only 3 domains
Map_af map(mgrid, r_limits) ;
// Construction of a flat metric
// -----------------------------
Metric_flat mets(map, map.get_bvect_spher()) ; // spherical representation
Metric_flat metc(map, map.get_bvect_cart()) ; // Cartesian representation
// Construction of a divergence free vector field
// ----------------------------------------------
const Coord& x = map.x ;
const Coord& y = map.y ;
const Coord& z = map.z ;
const Coord& r = map.r ;
const Coord& cost = map.cost ;
const Coord& sint = map.sint ;
const Coord& cosp = map.cosp ;
const Coord& sinp = map.sinp ;
cout << "========================================================" << endl ;
cout << " Test with a pretty general vector" << endl ;
cout << " V = curl(A) " << endl ;
cout << "========================================================" << endl ;
Vector aa(map, CON, map.get_bvect_cart()) ;
aa.set(1) = z * (x + x*y - 3*z*z) ;
aa.set(2) = z * ( z*z*x - 2 *y + 1 );
aa.set(3) = 1 + x*x - y + x + x*y + z*z ;
aa.annule_domain(nzm1) ;
Mtbl tced = cost * ( sint*cosp/r + sint*sint*cosp*sinp - 3*cost*cost )
/ (r*r*r) ;
tced = cost / (r*r*r) ;
aa.set(1).set_domain(nzm1) = tced(nzm1) ;
tced = cost * ( cost*cost*sint*cosp - 2*sint*sinp / r + 1) / (r*r*r) ;
// aa.set(2).set_domain(nzm1) = tced(nzm1) ;
// tced = (1 + sint*sint*cosp*cosp / r - sint*sinp + sint*cosp*sint*sinp
// + cost*cost) / (r*r*r) ;
tced = cost*cost*sint*sinp / (r*r*r) ;
aa.set(3).set_domain(nzm1) = tced(nzm1) ;
aa.std_spectral_base() ;
aa.set(1).set_spectral_va().set_base_r(0, R_CHEBPIM_I) ;
aa.set(1).set_spectral_va().set_base_t(T_COSSIN_CI) ;
aa.set(2).set_spectral_va().set_base_r(0, R_CHEBPIM_I) ;
aa.set(2).set_spectral_va().set_base_t(T_COSSIN_CI) ;
aa.set(3).set_spectral_va().set_base_r(0, R_CHEBPIM_P) ;
aa.set(3).set_spectral_va().set_base_t(T_COSSIN_CP) ;
cout << "aa : " << endl ;
aa.spectral_display() ;
arrete() ;
// Curl of aa:
Vector_divfree vvc(map, map.get_bvect_cart(), metc ) ;
vvc.set(1) = aa(3).dsdy() - aa(2).dsdz() ;
vvc.set(2) = aa(1).dsdz() - aa(3).dsdx() ;
vvc.set(3) = aa(2).dsdx() - aa(1).dsdy() ;
cout << "Cartesian components : vvc : " << endl ;
vvc.spectral_display() ;
arrete() ;
Vector_divfree vvs = vvc ;
vvs.change_triad( map.get_bvect_spher() ) ;
cout << "Spherical components : vvs : " << endl ;
vvs.spectral_display() ;
arrete() ;
vvs.inc_dzpuis(2) ;
cout << "vvs after inc_dzpuis(2) : " << endl ;
vvs.spectral_display() ;
cout << "mu : " << endl ;
cout << "----" << endl ;
vvs.mu().spectral_display() ;
Vector_divfree wws = vvs.poisson() ;
cout << "Solution wws : " << endl ;
wws.spectral_display() ;
arrete() ;
Vector wwc = wws ;
wwc.change_triad( map.get_bvect_cart() ) ;
cout << "Max divergence wwc : " << max( abs(wwc.divergence(metc)) ) << endl ;
cout << "Max divergence wws : " << max( abs(wws.divergence(mets)) ) << endl ;
arrete() ;
Vector vdiff(map, CON, map.get_bvect_cart() ) ;
vdiff.set(1) = wwc(1).laplacian(2) - vvc(1) ; // dzpuis = 2
vdiff.set(2) = wwc(2).laplacian(2) - vvc(2) ;
vdiff.set(3) = wwc(3).laplacian(2) - vvc(3) ;
cout << "vdiff : " << endl ;
vdiff.spectral_display() ;
cout << "Max of vdiff : " << endl ;
for (int i=1; i<=3; i++) {
cout << max(abs(vdiff(i))) << endl ;
}
return EXIT_SUCCESS ;
}
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