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/*
* Methods of class Tslice_dirac_max for solving Einstein equations
*
* (see file time_slice.h for documentation).
*
*/
/*
* Copyright (c) 2004 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 tslice_dirac_max_solve_C[] = "$Header: /cvsroot/Lorene/C++/Source/Time_slice/tslice_dirac_max_solve.C,v 1.18 2014/10/13 08:53:48 j_novak Exp $" ;
/*
* $Id: tslice_dirac_max_solve.C,v 1.18 2014/10/13 08:53:48 j_novak Exp $
* $Log: tslice_dirac_max_solve.C,v $
* Revision 1.18 2014/10/13 08:53:48 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.17 2014/10/06 15:13:22 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.16 2010/10/20 07:58:10 j_novak
* Better implementation of the explicit time-integration. Not fully-tested yet.
*
* Revision 1.15 2008/12/02 15:02:22 j_novak
* Implementation of the new constrained formalism, following Cordero et al. 2009
* paper. The evolution eqs. are solved as a first-order system. Not tested yet!
*
* Revision 1.14 2004/07/08 12:29:01 j_novak
* use of new method Tensor::annule_extern_cn
*
* Revision 1.13 2004/06/30 08:02:40 j_novak
* Added filtering in l of khi_new and mu_new. ki_source is forced to go to
* zero at least as r^2.
*
* Revision 1.12 2004/06/17 07:07:11 e_gourgoulhon
* Method solve_hij:
* -- replaced the attenuation of khi_source with tempo by a call to
* the new method Tensor::annule_extern_c2
* -- suppressed filtre_r on khi_source and khi_new
* -- added graphs of W^i and LW^{ij} (transverse decomp of S^ij).
*
* Revision 1.11 2004/06/15 09:43:36 j_novak
* Attenuation of the source for khi in the last shell (temporary?).
*
* Revision 1.10 2004/06/14 20:47:31 e_gourgoulhon
* Added argument method_poisson to method solve_hij.
*
* Revision 1.9 2004/06/03 10:02:45 j_novak
* Some filtering is done on source_khi and khi_new.
*
* Revision 1.8 2004/05/24 21:00:44 e_gourgoulhon
* Method solve_hij: khi and mu.smooth_decay(2,2) --> smooth_decay(2,1) ;
* added exponential_decay(khi) and exponential_decay(mu) after the
* call to smooth_decay. Method exponential_decay is provisory defined
* in this file.
*
* Revision 1.7 2004/05/17 19:56:25 e_gourgoulhon
* -- Method solve_beta: added argument method
* -- Method solve_hij: added argument graph_device
*
* Revision 1.6 2004/05/12 15:24:20 e_gourgoulhon
* Reorganized the #include 's, taking into account that
* time_slice.h contains now an #include "metric.h".
*
* Revision 1.5 2004/05/05 14:47:05 e_gourgoulhon
* Modified text and graphical outputs.
*
* Revision 1.4 2004/05/03 15:06:27 e_gourgoulhon
* Added matter source in solve_hij.
*
* Revision 1.3 2004/05/03 14:50:00 e_gourgoulhon
* Finished the implementation of method solve_hij.
*
* Revision 1.2 2004/04/30 14:36:15 j_novak
* Added the method Tslice_dirac_max::solve_hij(...)
* NOT READY YET!!!
*
* Revision 1.1 2004/04/30 10:52:14 e_gourgoulhon
* First version.
*
*
* $Header: /cvsroot/Lorene/C++/Source/Time_slice/tslice_dirac_max_solve.C,v 1.18 2014/10/13 08:53:48 j_novak Exp $
*
*/
// C headers
#include <cassert>
// Lorene headers
#include "time_slice.h"
#include "unites.h"
#include "graphique.h"
#include "proto.h"
//----------------------------//
// Equation for N\Psi //
//----------------------------//
namespace Lorene {
Scalar Tslice_dirac_max::solve_npsi(const Scalar* p_ener_dens,
const Scalar* p_trace_stress) const {
using namespace Unites ;
const Map& map = npsi().get_mp() ;
Scalar ener_dens(map) ;
if (p_ener_dens != 0x0) ener_dens = *(p_ener_dens) ;
else ener_dens.set_etat_zero() ;
Scalar trace_stress(map) ;
if (p_trace_stress != 0x0) trace_stress = *(p_trace_stress) ;
else trace_stress.set_etat_zero() ;
// Source for N\Psi
// ----------------
const Vector& dnpsi = npsi().derive_cov(ff) ; // D_i N\Psi
const Tensor_sym& dhh = hh().derive_cov(ff) ; // D_k h^{ij}
const Tensor_sym& dtgam = tgam().cov().derive_cov(ff) ;
// D_k {\tilde \gamma}_{ij}
Sym_tensor taa = aa().up_down(tgam()) ;
Scalar aa_quad = contract(taa, 0, 1, aa(), 0, 1) ;
Scalar tildeR = 0.25 * contract( dhh, 0, 1, dtgam, 0, 1 ).trace(tgam())
- 0.5 * contract( dhh, 0, 1, dtgam, 0, 2 ).trace(tgam()) ;
Scalar source_npsi = - contract( hh(), 0, 1, dnpsi.derive_cov(ff), 0, 1 ) ;
source_npsi.inc_dzpuis() ;
source_npsi += npsi()*( 0.5*qpig*(ener_dens + 2.*trace_stress )/( psi()*psi() )
+ 0.875*aa_quad/( psi4()*psi4() ) + 0.125*tildeR ) ;
// Resolution of the Poisson equation for N\Psi
// --------------------------------------------
Scalar npsi_new = source_npsi.poisson() + 1. ;
if (npsi_new.get_etat() == ETATUN) npsi_new.std_spectral_base() ;
#ifndef NDEBUG
// Test:
maxabs(npsi_new.laplacian() - source_npsi,
"Absolute error in the resolution of the equation for N") ;
#endif
return npsi_new ;
}
//--------------------------//
// Equation for \Psi //
//--------------------------//
Scalar Tslice_dirac_max::solve_psi(const Scalar* p_ener_dens) const {
using namespace Unites ;
const Map& map = psi().get_mp() ;
Scalar ener_dens(map) ;
if (p_ener_dens != 0x0) ener_dens = *(p_ener_dens) ;
else ener_dens.set_etat_zero() ;
// Source for \Psi
// ---------------
const Vector& dpsi = psi().derive_cov(ff) ; // D_i Psi
const Tensor_sym& dhh = hh().derive_cov(ff) ; // D_k h^{ij}
const Tensor_sym& dtgam = tgam().cov().derive_cov(ff) ;
// D_k {\tilde \gamma}_{ij}
Sym_tensor taa = hata().up_down(tgam()) ;
Scalar aa_quad = contract(taa, 0, 1, hata(), 0, 1) ;
Scalar tildeR = 0.25 * contract( dhh, 0, 1, dtgam, 0, 1 ).trace(tgam())
- 0.5 * contract( dhh, 0, 1, dtgam, 0, 2 ).trace(tgam()) ;
Scalar source_psi = -contract( hh(), 0, 1, dpsi.derive_cov(ff), 0, 1 ) ;
source_psi.inc_dzpuis() ;
source_psi -= 0.5*qpig*ener_dens/psi()
+ 0.125*( aa_quad*pow(psi(), -7) - tildeR*psi() ) ;
// Resolution of the Poisson equation for Psi
// ------------------------------------------
Scalar psi_new = source_psi.poisson() + 1. ;
if (psi_new.get_etat() == ETATUN) psi_new.std_spectral_base() ;
#ifndef NDEBUG
// Test:
maxabs(psi_new.laplacian() - source_psi,
"Absolute error in the resolution of the equation for Psi") ;
#endif
return psi_new ;
}
//--------------------------//
// Equation for beta //
//--------------------------//
Vector Tslice_dirac_max::solve_beta(int method)
const {
// Source for beta
// ---------------
Vector source_beta =
- contract(hh(), 0, 1, beta().derive_cov(ff).derive_cov(ff), 1, 2)
- 0.3333333333333333*contract(hh(), 1, beta().divergence(ff).derive_cov(ff), 0) ;
Sym_tensor sym_tmp = 2*nn()*aa() ;
source_beta += sym_tmp.divergence(ff) ;
source_beta.inc_dzpuis() ; // dzpuis: 3 -> 4
// Resolution of the vector Poisson equation
//------------------------------------------
Vector beta_new = source_beta.poisson(0.3333333333333333, ff, method) ;
#ifndef NDEBUG
// Test:
Vector test_beta = (beta_new.derive_con(ff)).divergence(ff)
+ 0.3333333333333333 * (beta_new.divergence(ff)).derive_con(ff) ;
test_beta.inc_dzpuis() ;
maxabs(test_beta - source_beta,
"Absolute error in the resolution of the equation for beta") ;
#endif
return beta_new ;
}
}
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