/usr/include/lorene/C++/Include/app_hor.h is in liblorene-dev 0.0.0~cvs20161116+dfsg-1ubuntu4.
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* Definition of Lorene class App_hor
*
*/
/*
* Copyright (c) 2005 Lap-Ming Lin & 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
*
*/
#ifndef __APP_HOR_H_
#define __APP_HOR_H_
/*
* $Id: app_hor.h,v 1.6 2014/10/13 08:52:31 j_novak Exp $
* $Log: app_hor.h,v $
* Revision 1.6 2014/10/13 08:52:31 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.5 2012/01/02 13:52:57 j_novak
* New parameter 'verbose' to get less output if needed.
*
* Revision 1.4 2005/12/09 09:35:59 lm_lin
*
* Minor fix in the documentation.
*
* Revision 1.3 2005/12/07 11:11:30 lm_lin
*
* Add option to turn off screen output during iterations.
*
* Revision 1.2 2005/11/17 14:19:49 lm_lin
*
* Check the expansion function evaluated on the apparent horizon after the
* iteration of the 2-surface converges.
*
* Revision 1.1 2005/10/13 08:51:14 j_novak
* New stuff for apparent horizon finder. For the moment, there is only an
* external function. A class should come soon...
*
* $Header: /cvsroot/Lorene/C++/Include/app_hor.h,v 1.6 2014/10/13 08:52:31 j_novak Exp $
*
*/
// Headers Lorene
#include "metric.h"
namespace Lorene {
/**
* Class for apparent horizon (under heavy development)
*
*/
// Function (Apparent horizon finder)
//-----------------------------------------------
/**
* Apparent horizon finder. \ingroup (star)
*
* Find the apparent horizon (AH) on a spatial slice for given
* 3-metric \f$\gamma_{ij}\f$ and extrinsic curvature \f$K_{ij}\f$.
* Method: We solve the apparent-horizon equation
* \f$\Theta=0\f$ (where \f$\Theta\f$ is the expansion function
* of the outgoing null geodesic) as a generalized angular Poisson
* equation (\f$\Delta_{\theta\phi}u+\lambda u=\sigma\f$) in the form:
*
* \f[
* \Delta_{\theta\phi}h - 2h = \Psi^4 |DF| h^2\Theta +
* \Delta_{\theta\phi}h - 2h
* \f]
*
* where \f$h=h(\theta,\phi)\f$ (\c h) is the 2-surface of the AH,
* \f$\Psi\f$ is the conformal factor, and
* \f$|DF|:= (\gamma^{ij}D_iFD_jF)^{1/2} \f$ (where \f$F\f$ is the
* level set function \f$ F:=r-h(\theta,\phi) \f$ and \f$D_i\f$ is the
* covariant derivative w.r.t. \f$\gamma_{ij}\f$).
* We solve the above equation iteratively with the right hand side
* of the equation as a source term.
*
* @param gamma : [input] the 3-metric \f$\gamma_{ij}\f$ w.r.t. which
* the AH is to be found.
* @param k_dd_in : [input] the extrinsic curvature \f$K_{ij}\f$.
* @param Valeur h : [output] the 2-surface of the apparent horizon
* @param Scalar ex_fcn : [output] the expansion function defined from
* the level set function \f$F:= r - h(\theta,\phi)\f$
* @param a_axis : [input] the initial guess for \f$h\f$ is a triaxial
* ellipsoidal surface with a_axis the axis along the x-axis of
* the Cartesian grid
* @param b_axis : [input] axis along the y-axis (cf a_axis)
* @param c_axis : [input] axis along the z-axis (cf a_axis)
* @param bool print : [input] screen printout during iterations? (default: false)
* @param precis : [input] threshold in the relative difference between
* the 2-surface \f$h\f$ of two consecutive steps to stop
* the iterative procedure (default value: 1.e-8)
* @param precis_exp : [input] maximum error of the expansion function evaluated on
* the 2-surface \f$h\f$ (should be zero by definition) after the iteration
* is stopped (default value: 1.e-6)
* @param it_max : [input] maximum number of steps (default value: 200)
* @param it_relax : [input] step at which relaxation is switched on
* (default value: 200)
* @param relax_fac : [input] relaxation factor (default value:
* 1 for no relaxation)
* @return bool ah_flag : a flag to indicate whether an apparent horizon is found
*/
bool ah_finder(const Metric& gamma, const Sym_tensor& k_dd_in, Valeur& h, Scalar& ex_fcn,
double a_axis, double b_axis, double c_axis, bool verbose = true,
bool print = false, double precis = 1.e-8, double precis_exp = 1.e-6,
int it_max = 200, int it_relax = 200, double relax_fac = 1.) ;
}
#endif
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