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/*
* Code for testing the angular Poisson equation.
*
*/
/*
* Copyright (c) 2003-2005 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_poisson_angu_C[] = "$Header: /cvsroot/Lorene/Codes/Test/Tensor/test_poisson_angu.C,v 1.6 2014/10/13 08:54:03 j_novak Exp $" ;
/*
* $Id: test_poisson_angu.C,v 1.6 2014/10/13 08:54:03 j_novak Exp $
* $Log: test_poisson_angu.C,v $
* Revision 1.6 2014/10/13 08:54:03 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.5 2014/10/06 15:12:55 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.4 2005/05/18 15:31:25 j_novak
* *** empty log message ***
*
* Revision 1.3 2005/04/04 21:36:31 e_gourgoulhon
* Method Scalar::poisson_angu takes now a parameter
* lambda, for the generalized angular Poisson equation
* Lap_ang u + lambda u = source.
* Test passed for lambda = 1 and lambda = 10.
*
* Revision 1.2 2003/10/19 20:05:07 e_gourgoulhon
* Change of the argument list of Scalar::spectral_display
* (cout now default).
*
* Revision 1.1 2003/10/15 21:15:25 e_gourgoulhon
* Test for Scalar::poisson_angu().
*
*
*
* $Header: /cvsroot/Lorene/Codes/Test/Tensor/test_poisson_angu.C,v 1.6 2014/10/13 08:54:03 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 nr = 5 ; // Number of collocation points in r in each domain
int nt = 5 ; // 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., 1., 2., __infinity} ;
assert( nz == 3 ) ; // since the above array described only 3 domains
Map_af map(mgrid, r_limits) ;
cout << endl <<
"================ TEST FOR A SCALAR FIELD =================\n" ;
// Construction of a scalar field (Scalar)
// ---------------------------------------
const Coord& x = map.x ;
const Coord& y = map.y ;
const Coord& z = map.z ;
const Coord& r = map.r ;
const Coord& sint = map.sint ;
const Coord& sinp = map.sinp ;
Scalar uu(map) ;
Scalar tmp(map) ;
uu = x + y + x*y + z*z*x - pow(z,4)*y*x ;
tmp = sint * sinp / r ;
uu.set_domain(nz-1) = tmp.domain(nz-1) ; // y/r^2 in the external domain
uu.std_spectral_base() ; // sets the standard spectral basis for
// expansion of a scalar field
cout << "uu : " << uu << endl ;
uu.spectral_display() ;
arrete() ;
double lambda = 2. ;
Scalar lap = uu.lapang() ;
lap.set_spectral_va().ylm_i() ;
lap += lambda * uu ;
cout << "lap : " << endl ;
lap.spectral_display() ;
arrete() ;
Scalar uu1 = lap.poisson_angu(lambda) ;
cout << "uu1 : " << endl ;
uu1.spectral_display() ;
arrete() ;
Scalar diff = uu - uu1 ;
diff.set_spectral_va().ylm() ;
diff.spectral_display("Diff en Ylm: ", 1.e-14) ;
cout << "Norm of diff: " << norme(diff) << endl ;
return EXIT_SUCCESS ;
}
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