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/*
* Resolution of a simple Poisson equation.
*
*/
/*
* Copyright (c) 2004 Eric Gourgoulhon
*
* 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 simple_poisson_C[] = "$Header: /cvsroot/Lorene/Codes/Tutorial/simple_poisson.C,v 1.7 2014/10/13 08:54:03 j_novak Exp $" ;
/*
* $Id: simple_poisson.C,v 1.7 2014/10/13 08:54:03 j_novak Exp $
* $Log: simple_poisson.C,v $
* Revision 1.7 2014/10/13 08:54:03 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.6 2007/12/20 09:11:10 jl_cornou
* Correction of an error in op_sxpun about Jacobi(0,2) polynomials
*
* Revision 1.5 2007/12/11 15:28:27 jl_cornou
* Jacobi(0,2) polynomials partially implemented
*
* Revision 1.4 2005/03/25 20:29:57 e_gourgoulhon
* Use of new graphical routines for Scalar and Vector.
*
* Revision 1.3 2004/02/27 21:19:12 e_gourgoulhon
* Benefits from the fact that now derive_cov applied to a scalar
* returns a reference on a Vector (treatment of dpot).
*
* Revision 1.2 2004/02/16 13:00:00 e_gourgoulhon
* Added the C headers (not required by GNU g++ !!!).
*
* Revision 1.1 2004/02/15 22:08:16 e_gourgoulhon
* The example with Poisson equation is now in file simple_poisson.C.
* simple_wave.C contains now an example of resolution of d'Alembert
* equation. The time evolution is managed thanks to the new
* class Evolution_std.
*
*
*
* $Header: /cvsroot/Lorene/Codes/Tutorial/simple_poisson.C,v 1.7 2014/10/13 08:54:03 j_novak Exp $
*
*/
// C++ headers
#include "headcpp.h"
// C headers
#include "stdlib.h"
#include "assert.h"
#include "math.h"
// Lorene headers
#include "nbr_spx.h"
#include "tensor.h"
#include "metric.h"
#include "graphique.h"
#include "utilitaires.h"
using namespace Lorene ;
int main() {
// Setup of a multi-domain grid (Lorene class Mg3d)
// ------------------------------------------------
int nz = 3 ; // Number of domains
int nr = 7 ; // Number of collocation points in r in each domain
int nt = 5 ; // Number of collocation points in theta in each domain
int np = 8 ; // 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
// Multi-domain grid construction:
Mg3d mgrid(nz, nr, nt, np, symmetry_theta, symmetry_phi, compact) ;
cout << mgrid << endl ;
// Setup of an affine mapping : grid --> physical space (Lorene class Map_af)
// --------------------------------------------------------------------------
// radial boundaries of each domain:
double r_limits[] = {0., 2., 3., __infinity} ;
assert( nz == 3 ) ; // since the above array described only 3 domains
Map_af map(mgrid, r_limits) ; // Mapping construction
cout << map << endl ;
// Denomination of various coordinates associated with the mapping
// ---------------------------------------------------------------
const Coord& r = map.r ; // r field
const Coord& th = map.tet ; // theta field
const Coord& phi = map.phi ; // phi field
const Coord& x = map.x ; // x field
const Coord& y = map.y ; // y field
const Coord& z = map.z ; // z field
// Setup of a scalar field (source of the Poisson equation)
// --------------------------------------------------------
Scalar source(map) ; // construction of an object of Lorene class Scalar
source = 2* exp( - r*r ) * (1 + x + x*y) ;
source.annule_domain(nz-1) ; // The source is set to zero in the last
// domain
source.std_spectral_base() ; // sets the bases for the spectral expansions
// to the standard ones for a scalar field
cout << source << endl ; // prints to screen
source.spectral_display() ; // prints the spectral expansions
// 1-D visualization via PGPLOT
// ----------------------------
des_meridian(source, 0., 1.1* r_limits[nz-1], "source", 1) ;
arrete() ;
// 2-D visualization via PGPLOT
// ----------------------------
des_coupe_z(source, 0., 2, "Source") ;
// 3-D visualization via OpenDX
// ----------------------------
double z0 = 0 ; // section plane : z = z0
source.visu_section('z', z0, -2., 2., -1.5, 1.5, "Example of section vis.") ;
source.visu_box(-2., 2., -1.5, 1.5, -1., 1., "Example of volume rendering", 0x0) ;
// Resolution of a Poisson equation
// --------------------------------
Scalar pot = source.poisson() ;
cout << "Solution of the Poisson equation : " << endl ;
pot.spectral_display() ; // prints the spectral expansions
des_coupe_z( pot, 0., 2, "Potential") ;
// pot.visu_section('z', z0, -2., 2., -1.5, 1.5, "Potential", "pot") ;
// 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
// Gradient of the potential
// -------------------------
Vector dpot = pot.derive_cov(metc) ;
dpot.dec_dzpuis(2) ;
des_coupe_vect_z(dpot, 0., -2., 0.5, 2, "Gradient of potential") ;
dpot.visu_arrows(-1., 1., -1., 1., -1., 1., "Gradient of potential",
"gradient") ;
return EXIT_SUCCESS ;
}
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