/usr/include/lorene/C++/Include/map.h is in liblorene-dev 0.0.0~cvs20161116+dfsg-1ubuntu4.
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The actual contents of the file can be viewed below.
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* Definition of Lorene classes Map
* Map_radial
* Map_af
* Map_et
* Map_log
*
*/
/*
* Copyright (c) 1999-2000 Jean-Alain Marck
* Copyright (c) 1999-2003 Eric Gourgoulhon
* Copyright (c) 1999-2001 Philippe Grandclement
* Copyright (c) 2000-2001 Jerome Novak
* Copyright (c) 2000-2001 Keisuke Taniguchi
*
* 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 as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* 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 __MAP_H_
#define __MAP_H_
/*
* $Id: map.h,v 1.59 2014/10/13 08:52:35 j_novak Exp $
* $Log: map.h,v $
* Revision 1.59 2014/10/13 08:52:35 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.58 2014/10/06 15:09:40 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.57 2014/01/14 13:24:02 b_peres
* *** empty log message ***
*
* Revision 1.56 2012/01/24 14:58:54 j_novak
* Removed functions XXX_fait_xi()
*
* Revision 1.55 2012/01/17 15:34:20 j_penner
* *** empty log message ***
*
* Revision 1.54 2012/01/17 10:20:07 j_penner
* added a member cxi that allows for direct access to the computational coordinates in each domain
*
* Revision 1.53 2008/09/29 13:23:51 j_novak
* Implementation of the angular mapping associated with an affine
* mapping. Things must be improved to take into account the domain index.
*
* Revision 1.52 2007/10/16 21:52:10 e_gourgoulhon
* Added method poisson_compact for multi-domains.
*
* Revision 1.51 2007/05/15 12:44:18 p_grandclement
* Scalar version of reevaluate
*
* Revision 1.50 2007/05/06 10:48:08 p_grandclement
* Modification of a few operators for the vorton project
*
* Revision 1.49 2007/01/16 15:05:59 n_vasset
* New constructor (taking a Scalar in mono-domain angular grid for
* boundary) for function sol_elliptic_boundary
*
* Revision 1.48 2006/08/31 12:10:51 j_novak
* More comments for Map_af::avance_dalembert().
*
* Revision 1.47 2006/05/26 09:00:09 j_novak
* New members for multiplication or division by cos(theta).
*
* Revision 1.46 2006/04/25 07:21:54 p_grandclement
* Various changes for the NS_BH project
*
* Revision 1.45 2005/11/30 11:09:03 p_grandclement
* Changes for the Bin_ns_bh project
*
* Revision 1.44 2005/11/24 09:25:06 j_novak
* Added the Scalar version for the Laplacian
*
* Revision 1.43 2005/09/15 15:51:25 j_novak
* The "rotation" (change of triad) methods take now Scalars as default
* arguments.
*
* Revision 1.42 2005/08/26 14:02:38 p_grandclement
* Modification of the elliptic solver that matches with an oscillatory exterior solution
* small correction in Poisson tau also...
*
* Revision 1.41 2005/08/25 12:14:07 p_grandclement
* Addition of a new method to solve the scalar Poisson equation, based on a multi-domain Tau-method
*
* Revision 1.40 2005/06/09 07:56:24 f_limousin
* Implement a new function sol_elliptic_boundary() and
* Vector::poisson_boundary(...) which solve the vectorial poisson
* equation (method 6) with an inner boundary condition.
*
* Revision 1.39 2005/04/04 21:30:41 e_gourgoulhon
* Added argument lambda to method poisson_angu
* to treat the generalized angular Poisson equation:
* Lap_ang u + lambda u = source.
*
* Revision 1.38 2004/12/29 16:37:22 k_taniguchi
* Addition of some functions with the multipole falloff condition.
*
* Revision 1.37 2004/12/02 09:33:04 p_grandclement
* *** empty log message ***
*
* Revision 1.36 2004/11/30 20:42:05 k_taniguchi
* Addition of some functions with the falloff condition and a method
* to resize the external shell.
*
* Revision 1.35 2004/11/23 12:39:12 f_limousin
* Intoduce function poisson_dir_neu(...) to solve a scalar poisson
* equation with a mixed boundary condition (Dirichlet + Neumann).
*
* Revision 1.34 2004/10/11 15:08:59 j_novak
* The radial manipulation functions take Scalar as arguments, instead of Cmp.
* Added a conversion operator from Scalar to Cmp.
* The Cmp radial manipulation function make conversion to Scalar, call to the
* Map_radial version with a Scalar argument and back.
*
* Revision 1.33 2004/10/08 13:34:35 j_novak
* Scalar::div_r() does not need to pass through Cmp version anymore.
*
* Revision 1.32 2004/08/24 09:14:40 p_grandclement
* Addition of some new operators, like Poisson in 2d... It now requieres the
* GSL library to work.
*
* Also, the way a variable change is stored by a Param_elliptic is changed and
* no longer uses Change_var but rather 2 Scalars. The codes using that feature
* will requiere some modification. (It should concern only the ones about monopoles)
*
* Revision 1.31 2004/07/27 08:24:26 j_novak
* Modif. comments
*
* Revision 1.30 2004/07/26 16:02:21 j_novak
* Added a flag to specify whether the primitive should be zero either at r=0
* or at r going to infinity.
*
* Revision 1.29 2004/06/22 08:49:57 p_grandclement
* Addition of everything needed for using the logarithmic mapping
*
* Revision 1.28 2004/06/14 15:23:53 e_gourgoulhon
* Added virtual function primr for computation of radial primitives.
*
* Revision 1.27 2004/03/31 11:22:23 f_limousin
* Methods Map_et::poisson_interne and Map_af::poisson_interne have been
* implemented to solve the continuity equation for strange stars.
*
* Revision 1.26 2004/03/22 13:12:41 j_novak
* Modification of comments to use doxygen instead of doc++
*
* Revision 1.24 2004/03/01 09:57:02 j_novak
* the wave equation is solved with Scalars. It now accepts a grid with a
* compactified external domain, which the solver ignores and where it copies
* the values of the field from one time-step to the next.
*
* Revision 1.23 2004/02/11 09:47:44 p_grandclement
* Addition of a new elliptic solver, matching with the homogeneous solution
* at the outer shell and not solving in the external domain (more details
* coming soon ; check your local Lorene dealer...)
*
* Revision 1.22 2004/01/29 08:50:01 p_grandclement
* Modification of Map::operator==(const Map&) and addition of the surface
* integrales using Scalar.
*
* Revision 1.21 2004/01/28 16:46:22 p_grandclement
* Addition of the sol_elliptic_fixe_der_zero stuff
*
* Revision 1.20 2004/01/28 10:35:52 j_novak
* Added new methods mult_r() for Scalars. These do not change the dzpuis flag.
*
* Revision 1.19 2004/01/27 09:33:46 j_novak
* New method Map_radial::div_r_zec
*
* Revision 1.18 2004/01/26 16:16:15 j_novak
* Methods of gradient for Scalar s. The input can have any dzpuis.
*
* Revision 1.17 2004/01/19 21:38:21 e_gourgoulhon
* Corrected sign error in comments of Map_radial::dxdr.
*
* Revision 1.16 2003/12/30 22:52:47 e_gourgoulhon
* Class Map: added methods flat_met_spher() and flat_met_cart() to get
* flat metric associated with the coordinates described by the mapping.
*
* Revision 1.15 2003/12/11 14:48:47 p_grandclement
* Addition of ALL (and that is a lot !) the files needed for the general elliptic solver ... UNDER DEVELOPEMENT...
*
* Revision 1.14 2003/11/06 14:43:37 e_gourgoulhon
* Gave a name to const arguments in certain method prototypes (e.g.
* constructors) to correct a bug of DOC++.
*
* Revision 1.13 2003/11/04 22:54:49 e_gourgoulhon
* Added new virtual methods mult_cost, mult_sint and div_sint.
*
* Revision 1.12 2003/10/16 08:49:21 j_novak
* Added a flag to decide wether the output is in the Ylm or in the standard base.
*
* Revision 1.11 2003/10/15 21:08:22 e_gourgoulhon
* Added method poisson_angu.
*
* Revision 1.10 2003/10/15 16:03:35 j_novak
* Added the angular Laplace operator for Scalar.
*
* Revision 1.9 2003/10/15 10:27:33 e_gourgoulhon
* Classes Map, Map_af and Map_et: added new methods dsdt, stdsdp and div_tant.
* Class Map_radial: added new Coord's : drdt and stdrdp.
*
* Revision 1.8 2003/06/20 14:14:53 f_limousin
* Add the operator== to compare two Cmp.
*
* Revision 1.7 2003/06/20 09:27:09 j_novak
* Modif commentaires.
*
* Revision 1.6 2002/10/16 14:36:29 j_novak
* Reorganization of #include instructions of standard C++, in order to
* use experimental version 3 of gcc.
*
* Revision 1.5 2002/09/13 09:17:33 j_novak
* Modif. commentaires
*
* Revision 1.4 2002/06/17 14:05:16 j_novak
* friend functions are now also declared outside the class definition
*
* Revision 1.3 2002/05/07 07:06:37 e_gourgoulhon
* Compatibily with xlC compiler on IBM SP2:
* added declaration of functions map_af_fait_* and map_et_fait_*
* outside the classes declarations.
*
* Revision 1.2 2002/01/15 15:53:06 p_grandclement
* I have had a constructor fot map_et using the equation of the surface
* of the star.
*
* Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
* LORENE
*
* Revision 2.110 2001/10/29 15:31:55 novak
* Ajout de Map_radial::div_r
*
* Revision 2.109 2001/10/16 10:02:49 novak
* *** empty log message ***
*
* Revision 2.108 2001/07/19 14:01:00 novak
* new arguments for Map_af::dalembert
*
* Revision 2.107 2001/02/26 17:28:31 eric
* Ajout de la fonction virtuelle resize.
*
* Revision 2.106 2001/01/10 11:03:00 phil
* ajout de homothetie interne
*
* Revision 2.105 2001/01/02 10:51:55 phil
* ajout integrale de surface a l'infini
*
* Revision 2.104 2000/10/23 13:59:48 eric
* Map_et::adapt: changement des arguments (en autre, ajout de nz_search).
*
* Revision 2.103 2000/10/20 09:39:19 phil
* changement commentaires
*
* Revision 2.102 2000/10/19 14:33:23 novak
* corrige oubli pour Map_et?
*
* Revision 2.101 2000/10/19 14:11:20 novak
* Ajout des fonctions membres Map::dalembert et Map_af::dalembert
* (etat experimental)
*
* Revision 2.100 2000/10/09 13:46:39 eric
* Ajout de la fonction virtuelle poisson2d.
*
* Revision 2.99 2000/09/19 15:28:55 phil
* *** empty log message ***
*
* Revision 2.98 2000/09/19 15:24:19 phil
* ajout du passage de cartesienne en spheriques
*
* Revision 2.97 2000/09/19 13:05:38 phil
* ajout integrale_surface
*
* Revision 2.96 2000/09/11 15:54:03 eric
* Suppression des methodes deriv_x, deriv_y et deriv_z.
* Introduction des methodes comp_x_from_spherical, etc...
*
* Revision 2.95 2000/09/07 15:27:58 keisuke
* Add a new argument Cmp& uu in Map_af::poisson_regular and Map_et::poisson_regular.
*
* Revision 2.94 2000/09/04 15:30:56 keisuke
* Modify the arguments of Map_af::poisson_regular and Map_et::poisson_regular.
*
* Revision 2.93 2000/09/04 13:36:19 keisuke
* Modify the explanation for "uu_div" in Map_et::poisson_regular.
*
* Revision 2.92 2000/08/31 15:50:12 keisuke
* Modify Map_af::poisson_regular.
* Add Map_et::poisson_regular and Map::poisson_regular.
*
* Revision 2.91 2000/08/31 13:03:22 eric
* Ajout de la fonction virtuelle mult_rsint.
*
* Revision 2.90 2000/08/28 16:17:37 keisuke
* Add "int nzet" in the argumant of Map_af::poisson_regular.
*
* Revision 2.89 2000/08/18 11:10:12 eric
* Classe Map_et: ajout de l'operateur d'affectation a un autre Map_et.
*
* Revision 2.88 2000/08/11 08:50:18 keisuke
* Modif Map_af::poisson_regular
*
* Revision 2.87 2000/08/10 12:54:00 keisuke
* Ajout de Map_af::poisson_regular
*
* Revision 2.86 2000/07/20 14:21:07 eric
* Ajout de la fonction div_rsint.
*
* Revision 2.85 2000/05/25 13:54:41 eric
* Modif commentaires
*
* Revision 2.84 2000/05/22 14:38:51 phil
* ajout de inc_dzpuis et dec_dzpuis
*
* Revision 2.83 2000/04/27 15:18:54 phil
* *** empty log message ***
*
* Revision 2.82 2000/03/20 13:33:23 phil
* commentaires
*
* Revision 2.81 2000/03/17 17:32:48 phil
* *** empty log message ***
*
* Revision 2.80 2000/03/17 17:01:54 phil
* *** empty log message ***
*
* Revision 2.79 2000/03/17 16:58:48 phil
* ajout de poisson_frontiere
*
* Revision 2.78 2000/03/06 11:29:51 eric
* Ajout du membre reeavaluate_symy.
*
* Revision 2.77 2000/02/15 15:08:21 eric
* Changement du Param dans Map_et::adapt : fact_echelle est desormais
* passe en double_mod.
*
* Revision 2.76 2000/02/15 10:26:25 phil
* commentaire +
* suppression de poisson_vect et poisson_vect_oohara
*
* Revision 2.75 2000/02/11 13:37:43 eric
* Ajout de la fonction convert_absolute.
*
* Revision 2.74 2000/02/09 09:53:37 phil
* ajout de poisson_vect_oohara
*
* Revision 2.73 2000/01/26 13:07:02 eric
* Reprototypage complet des routines de derivation:
* le resultat est desormais suppose alloue a l'exterieur de la routine
* et est passe en argument (Cmp& resu), si bien que le prototypage
* complet devient:
* void DERIV(const Cmp& ci, Cmp& resu)
*
* Revision 2.72 2000/01/24 17:08:21 eric
* Class Map_af : suppression de la fonction convert.
* suppression du constructeur par convertion d'un Map_et.
* ajout du constructeur par conversion d'un Map.
*
* Revision 2.71 2000/01/24 16:41:43 eric
* Ajout de la fonction virtuelle operator=(const Map_af& ).
* Classe Map_af : ajout de la fonction convert(const Map& ).
*
* Revision 2.70 2000/01/21 12:48:34 phil
* changement prototypage de Map::poisson_vect
*
* Revision 2.69 2000/01/20 16:35:05 phil
* *** empty log message ***
*
* Revision 2.68 2000/01/20 15:44:42 phil
* *** empty log message ***
*
* Revision 2.67 2000/01/20 15:31:56 phil
* *** empty log message ***
*
* Revision 2.66 2000/01/20 14:18:06 phil
* *** empty log message ***
*
* Revision 2.65 2000/01/20 13:16:34 phil
* *** empty log message ***
*
* Revision 2.64 2000/01/20 12:51:24 phil
* *** empty log message ***
*
* Revision 2.63 2000/01/20 12:45:28 phil
* *** empty log message ***
*
* Revision 2.62 2000/01/20 12:40:27 phil
* *** empty log message ***
*
* Revision 2.61 2000/01/20 11:27:54 phil
* ajout de poisson_vect
*
* Revision 2.60 2000/01/13 15:31:55 eric
* Modif commentaires/
*
* Revision 2.59 2000/01/12 16:02:57 eric
* Modif commentaires poisson_compact.
*
* Revision 2.58 2000/01/12 12:54:23 eric
* Ajout du Cmp null, *p_cmp_zero, et de la methode associee cmp_zero().
*
* Revision 2.57 2000/01/10 13:27:43 eric
* Ajout des bases vectorielles associees aux coordonnees :
* membres bvect_spher et bvect_cart.
*
* Revision 2.56 2000/01/10 09:12:47 eric
* Reprototypage de poisson_compact : Valeur -> Cmp, Tenseur.
* Suppression de poisson_compact_boucle.
* poisson_compact est desormais implementee au niveau Map_radial.
*
* Revision 2.55 2000/01/04 15:23:11 eric
* Classe Map_radial : les data sont listees en premier
* Introduction de la fonction reevalutate.
*
* Revision 2.54 2000/01/03 13:30:32 eric
* Ajout de la fonction adapt.
*
* Revision 2.53 1999/12/22 17:09:52 eric
* Modif commentaires.
*
* Revision 2.52 1999/12/21 16:26:25 eric
* Ajout du constructeur par conversion Map_af::Map_af(const Map_et&).
* Ajout des fonctions Map_af::set_alpha et Map_af::set_beta.
*
* Revision 2.51 1999/12/21 13:01:29 eric
* Changement de prototype de la routine poisson : la solution est
* desormais passee en argument (et non plus en valeur de retour)
* pour permettre l'initialisation de methodes de resolution iterative.
*
* Revision 2.50 1999/12/21 10:12:09 eric
* Modif commentaires.
*
* Revision 2.49 1999/12/21 10:06:05 eric
* Ajout de l'argument Param& a poisson.
*
* Revision 2.48 1999/12/20 15:44:35 eric
* Modif commentaires.
*
* Revision 2.47 1999/12/20 10:47:45 eric
* Modif commentaires.
*
* Revision 2.46 1999/12/20 10:24:12 eric
* Ajout des fonctions de lecture des parametres de Map_et:
* get_alpha(), get_beta(), get_ff(), get_gg().
*
* Revision 2.45 1999/12/16 14:50:08 eric
* Modif commentaires.
*
* Revision 2.44 1999/12/16 14:17:54 eric
* Introduction de l'argument const Param& par dans val_lx et val_lx_jk.
* (en remplacement de l'argument Tbl& param).
*
* Revision 2.43 1999/12/09 10:45:24 eric
* Ajout de la fonction virtuelle integrale.
*
* Revision 2.42 1999/12/07 14:50:47 eric
* Changement ordre des arguments val_r, val_lx
* val_r_kj --> val_r_jk
* val_lx_kj -->val_lx_jk
*
* Revision 2.41 1999/12/06 16:45:20 eric
* Surcharge de val_lx avec la version sans param.
*
* Revision 2.40 1999/12/06 15:33:44 eric
* Ajout des fonctions val_r_kj et val_lx_kj.
*
* Revision 2.39 1999/12/06 13:11:54 eric
* Introduction des fonctions val_r, val_lx et homothetie.
*
* Revision 2.38 1999/12/02 14:28:22 eric
* Reprototypage de la fonction poisson: Valeur -> Cmp.
*
* Revision 2.37 1999/11/30 14:19:33 eric
* Reprototypage complet des fonctions membres mult_r, mult_r_zec,
* dec2_dzpuis et inc2_dzpuis : Valeur --> Cmp
*
* Revision 2.36 1999/11/29 13:17:57 eric
* Modif commentaires.
*
* Revision 2.35 1999/11/29 12:55:42 eric
* Changement prototype de la fonction laplacien : Valeur --> Cmp.
*
* Revision 2.34 1999/11/25 16:27:27 eric
* Reorganisation complete du calcul des derivees partielles.
*
* Revision 2.33 1999/11/24 16:31:17 eric
* Map_et: ajout des fonctions set_ff et set_gg.
*
* Revision 2.32 1999/11/24 14:31:48 eric
* Map_af: les membres alpha et beta deviennent prives.
* Map_af: introduction des fonctions get_alpha() et get_beta().
*
* Revision 2.31 1999/11/24 11:22:09 eric
* Map_et : Coords rendus publics
* Map_et : fonctions de constructions amies.
*
* Revision 2.30 1999/11/22 10:32:39 eric
* Introduction de la classe Map_et.
* Constructeurs de Map rendus protected.
* Fonction del_coord() rebaptisee reset_coord().
*
* Revision 2.29 1999/10/27 16:44:41 phil
* ajout de mult_r_zec
*
* Revision 2.28 1999/10/19 14:40:37 phil
* ajout de inc2_dzpuis()
*
* Revision 2.27 1999/10/15 14:12:20 eric
* *** empty log message ***
*
* Revision 2.26 1999/10/14 14:26:06 eric
* Depoussierage.
* Documentation.
*
* Revision 2.25 1999/10/11 11:16:29 phil
* changement prototypage de poisson_compact_boucle
*
* Revision 2.24 1999/10/11 10:48:51 phil
* changement de nom pour poisson a support compact
*
* Revision 2.23 1999/10/04 09:20:58 phil
* changement de prototypage de void Map_af::poisson_nul
*
* Revision 2.22 1999/09/30 18:38:32 phil
* *** empty log message ***
*
* Revision 2.21 1999/09/30 18:33:10 phil
* ajout de poisson_nul et poisson_nul_boucle
*
* Revision 2.20 1999/09/30 16:45:54 phil
* ajout de Map_af::poisson_nul(const Valeur&, int, int)
*
* Revision 2.19 1999/09/16 13:15:40 phil
* ajout de Valeur mult_r (const Valeur &)
*
* Revision 2.18 1999/09/15 10:42:11 phil
* ajout de Valeur dec2_dzpuis(const Valeur&)
*
* Revision 2.17 1999/09/14 13:45:45 phil
* suppression de la divergence
*
* Revision 2.16 1999/09/13 15:09:07 phil
* ajout de Map_af::divergence
*
* Revision 2.15 1999/09/13 13:52:23 phil
* ajout des derivations partielles par rapport a x,y et z.
*
* Revision 2.14 1999/09/07 14:35:20 phil
* ajout de la fonction Valeur** gradient(const Valeur&)
*
* Revision 2.13 1999/04/26 16:37:43 phil
* *** empty log message ***
*
* Revision 2.12 1999/04/26 16:33:28 phil
* *** empty log message ***
*
* Revision 2.11 1999/04/26 13:53:04 phil
* *** empty log message ***
*
* Revision 2.10 1999/04/26 13:51:19 phil
* ajout de Map_af::laplacien (2versions)
*
* Revision 2.9 1999/04/14 09:04:01 phil
* *** empty log message ***
*
* Revision 2.8 1999/04/14 08:53:27 phil
* *** empty log message ***
*
* Revision 2.7 1999/04/13 17:45:25 phil
* *** empty log message ***
*
* Revision 2.6 1999/04/13 17:02:41 phil
* ,
*
* Revision 2.5 1999/04/13 17:00:41 phil
* ajout de la resolution de poisson affine
*
* Revision 2.4 1999/03/04 13:10:53 eric
* Ajout des Coord representant les derivees du changement de variable
* dans la classe Map_radial.
*
* Revision 2.3 1999/03/01 17:00:38 eric
* *** empty log message ***
*
* Revision 2.2 1999/03/01 16:44:41 eric
* Operateurs << et >> sur les ostream.
* L'operateur >> est virtuel.
*
* Revision 2.1 1999/02/22 15:21:45 hyc
* *** empty log message ***
*
*
* Revision 2.0 1999/01/15 09:10:39 hyc
* *** empty log message ***
*
* $Header: /cvsroot/Lorene/C++/Include/map.h,v 1.59 2014/10/13 08:52:35 j_novak Exp $
*
*/
#include <cstdio>
#include "coord.h"
#include "base_vect.h"
#include "valeur.h"
#include "tbl.h"
#include "itbl.h"
namespace Lorene {
class Scalar ;
class Cmp ;
class Param ;
class Map_af ;
class Map_et ;
class Tenseur ;
class Param_elliptic ;
class Metric_flat ;
class Tbl ;
class Itbl ;
//------------------------------------//
// class Map //
//------------------------------------//
/**
* Base class for coordinate mappings. \ingroup (map)
*
* This class is the basic class for describing the mapping between the
* grid coordinates \f$(\xi, \theta', \phi')\f$ and the physical coordinates
* \f$(r, \theta, \phi)\f$ [cf. Bonazzola, Gourgoulhon & Marck, \e Phys.
* \e Rev. \e D \b 58, 104020 (1998)].
* The class \c Map is an abstract one: it cannot be instanciated.
* Specific implementation of coordinate mappings will be performed by derived
* classes of \c Map.
*
* The class \c Map and its derived classes determine the methods for
* partial derivatives with respect to the physical coordinates, as well
* as resolution of basic partial differential equations (e.g. Poisson
* equations).
*
* The mapping is defined with respect to some ``absolute'' reference frame,
* whose Cartesian coordinates are denoted by \e (X,Y,Z). The coordinates
* (X, Y, Z) of center of the mapping (i.e. the point \e r =0) are given by the data
* members \c (ori_x,ori_y,ori_z).
* The Cartesian coordinate relative to the mapping (i.e. defined from
* \f$(r, \theta, \phi)\f$ by the usual formul\ae \f$x=r\sin\theta\cos\phi, \ldots\f$)
* are denoted by \e (x,y,z). The planes \e (x,y) and \e (X,Y) are supposed to
* coincide, so that the relative orientation of the mapping with respect to
* the absolute reference frame is described by only one angle (the data member
* \c rot_phi).
*
*
*/
class Map {
// Data :
// ----
protected:
/// Pointer on the multi-grid \c Mgd3 on which \c this is defined
const Mg3d* mg ;
double ori_x ; ///< Absolute coordinate \e x of the origin
double ori_y ; ///< Absolute coordinate \e y of the origin
double ori_z ; ///< Absolute coordinate \e z of the origin
double rot_phi ; ///< Angle between the \e x --axis and \e X --axis
/** Orthonormal vectorial basis
* \f$(\partial/\partial r,1/r\partial/\partial \theta,
* 1/(r\sin\theta)\partial/\partial \phi)\f$
* associated with the coordinates \f$(r, \theta, \phi)\f$ of the
* mapping.
*/
Base_vect_spher bvect_spher ;
/** Cartesian basis
* \f$(\partial/\partial x,\partial/\partial y,\partial/\partial z)\f$
* associated with the coordinates \e (x,y,z) of the
* mapping, i.e. the Cartesian coordinates related to
* \f$(r, \theta, \phi)\f$ by means of usual formulae.
*/
Base_vect_cart bvect_cart ;
/** Pointer onto the flat metric associated with the spherical coordinates
* and with components expressed in the triad \c bvect_spher
*/
mutable Metric_flat* p_flat_met_spher ;
/** Pointer onto the flat metric associated with the Cartesian coordinates
* and with components expressed in the triad \c bvect_cart
*/
mutable Metric_flat* p_flat_met_cart ;
/** The null Cmp.
* To be used by the \c Tenseur class when necessary to
* return a null \c Cmp .
*/
Cmp* p_cmp_zero ;
mutable Map_af* p_mp_angu ; ///< Pointer on the "angular" mapping.
public:
Coord r ; ///< \e r coordinate centered on the grid
Coord tet ; ///< \f$\theta\f$ coordinate centered on the grid
Coord phi ; ///< \f$\phi\f$ coordinate centered on the grid
Coord sint ; ///< \f$\sin\theta\f$
Coord cost ; ///< \f$\cos\theta\f$
Coord sinp ; ///< \f$\sin\phi\f$
Coord cosp ; ///< \f$\cos\phi\f$
Coord x ; ///< \e x coordinate centered on the grid
Coord y ; ///< \e y coordinate centered on the grid
Coord z ; ///< \e z coordinate centered on the grid
Coord xa ; ///< Absolute \e x coordinate
Coord ya ; ///< Absolute \e y coordinate
Coord za ; ///< Absolute \e z coordinate
// Constructors, destructor :
// ------------------------
protected:
explicit Map(const Mg3d& ) ; ///< Constructor from a multi-domain 3D grid
Map(const Map &) ; ///< Copy constructor
Map(const Mg3d&, FILE* ) ; ///< Constructor from a file (see \c sauve(FILE* ) )
public:
virtual ~Map() ; ///< Destructor
// Memory management
// -----------------
protected:
virtual void reset_coord() ; ///< Resets all the member \c Coords
// Outputs
// -------
private:
virtual ostream& operator>>(ostream &) const = 0 ; ///< Operator >>
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
// Extraction of information
// -------------------------
public:
/// Gives the \c Mg3d on which the mapping is defined
const Mg3d* get_mg() const {return mg; };
/// Returns the \e x coordinate of the origin
double get_ori_x() const {return ori_x;} ;
/// Returns the \e y coordinate of the origin
double get_ori_y() const {return ori_y;} ;
/// Returns the \e z coordinate of the origin
double get_ori_z() const {return ori_z;} ;
/// Returns the angle between the \e x --axis and \e X --axis
double get_rot_phi() const {return rot_phi;} ;
/** Returns the orthonormal vectorial basis
* \f$(\partial/\partial r,1/r\partial/\partial \theta,
* 1/(r\sin\theta)\partial/\partial \phi)\f$
* associated with the coordinates \f$(r, \theta, \phi)\f$ of the
* mapping.
*/
const Base_vect_spher& get_bvect_spher() const {return bvect_spher;} ;
/** Returns the Cartesian basis
* \f$(\partial/\partial x,\partial/\partial y,\partial/\partial z)\f$
* associated with the coordinates \e (x,y,z) of the
* mapping, i.e. the Cartesian coordinates related to
* \f$(r, \theta, \phi)\f$ by means of usual formulae.
*/
const Base_vect_cart& get_bvect_cart() const {return bvect_cart;} ;
/** Returns the flat metric associated with the spherical coordinates
* and with components expressed in the triad \c bvect_spher
*/
const Metric_flat& flat_met_spher() const ;
/** Returns the flat metric associated with the Cartesian coordinates
* and with components expressed in the triad \c bvect_cart
*/
const Metric_flat& flat_met_cart() const ;
/** Returns the null \c Cmp defined on \c *this.
* To be used by the \c Tenseur class when necessary to
* return a null \c Cmp .
*/
const Cmp& cmp_zero() const {return *p_cmp_zero;} ;
/** Returns the "angular" mapping for the outside of domain \c l_zone.
* Valid only for the class \c Map_af.
*/
virtual const Map_af& mp_angu(int) const = 0 ;
/** Determines the coordinates \f$(r,\theta,\phi)\f$
* corresponding to given absolute Cartesian coordinates
* \e (X,Y,Z).
* @param xx [input] value of the coordinate \e x (absolute frame)
* @param yy [input] value of the coordinate \e y (absolute frame)
* @param zz [input] value of the coordinate \e z (absolute frame)
* @param rr [output] value of \e r
* @param theta [output] value of \f$\theta\f$
* @param pphi [output] value of \f$\phi\f$
*/
void convert_absolute(double xx, double yy, double zz,
double& rr, double& theta, double& pphi) const ;
/** Returns the value of the radial coordinate \e r for a given
* \f$(\xi, \theta', \phi')\f$ in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param theta [input] value of \f$\theta'\f$
* @param pphi [input] value of \f$\phi'\f$
* @return value of \f$r=R_l(\xi, \theta', \phi')\f$
*/
virtual double val_r(int l, double xi, double theta, double pphi)
const = 0 ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx(double rr, double theta, double pphi,
int& l, double& xi) const = 0 ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* This version enables to pass some parameters to control the
* accuracy of the computation.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param par [input/output] parameters to control the
* accuracy of the computation
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx(double rr, double theta, double pphi,
const Param& par, int& l, double& xi) const = 0 ;
/// Comparison operator (egality)
virtual bool operator==(const Map& ) const = 0;
// Modification of the origin, the orientation and the radial scale:
// ----------------------------------------------------------------
public:
void set_ori(double xa0, double ya0, double za0) ; ///< Sets a new origin
void set_rot_phi(double phi0) ; ///< Sets a new rotation angle
/** Sets a new radial scale.
* @param lambda [input] factor by which the value of \e r is to
* be multiplied
*/
virtual void homothetie(double lambda) = 0 ;
/** Rescales the outer boundary of one domain.
* The inner boundary is unchanged. The inner boundary
* of the next domain is changed to match the new outer
* boundary.
* @param l [input] index of the domain
* @param lambda [input] factor by which the value of
* \f$R(\theta, \varphi)\f$ defining the outer boundary
* of the domain is to be multiplied.
*/
virtual void resize(int l, double lambda) = 0 ;
// Modification of the mapping
// ---------------------------
public:
/// Assignment to an affine mapping.
virtual void operator=(const Map_af& ) = 0 ;
/** Adaptation of the mapping to a given scalar field.
* This is a virtual function: see the actual implementations
* in the derived classes for the meaning of the various
* parameters.
*/
virtual void adapt(const Cmp& ent, const Param& par, int nbr=0) = 0 ;
// Values of a Cmp at the new grid points
// --------------------------------------
/** Recomputes the values of a \c Cmp at the collocation points
* after a change in the mapping.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Cmp previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Cmp
* at the grid points defined by \c *this.
*/
virtual void reevaluate(const Map* mp_prev, int nzet,
Cmp& uu) const = 0 ;
/** Recomputes the values of a \c Cmp at the collocation points
* after a change in the mapping.
* Case where the \c Cmp is symmetric with respect the plane y=0.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Cmp previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Cmp
* at the grid points defined by \c *this.
*/
virtual void reevaluate_symy(const Map* mp_prev, int nzet,
Cmp& uu) const = 0 ;
/** Recomputes the values of a \c Scalar at the collocation points
* after a change in the mapping.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Scalar previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Scalae
* at the grid points defined by \c *this.
*/
virtual void reevaluate(const Map* mp_prev, int nzet,
Scalar& uu) const = 0 ;
/** Recomputes the values of a \c Scalar at the collocation points
* after a change in the mapping.
* Case where the \c Scalar is symmetric with respect the plane y=0.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Scalar previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Scalar
* at the grid points defined by \c *this.
*/
virtual void reevaluate_symy(const Map* mp_prev, int nzet,
Scalar& uu) const = 0 ;
// Differential operators:
// ----------------------
public:
/** Computes \f$\partial/ \partial \xi\f$ of a \c Cmp .
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = \xi^2 \partial/ \partial \xi\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdxi(const Cmp& ci, Cmp& resu) const = 0 ;
/** Computes \f$\partial/ \partial r\f$ of a \c Cmp .
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = r^2 \partial/ \partial r\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdr(const Cmp& ci, Cmp& resu) const = 0 ;
/** Computes \f$1/r \partial/ \partial \theta\f$ of a \c Cmp .
* Note that in the compactified external domain (CED), it computes
* \f$1/u \partial/ \partial \theta = r \partial/ \partial \theta\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void srdsdt(const Cmp& ci, Cmp& resu) const = 0 ;
/** Computes \f$1/(r\sin\theta) \partial/ \partial \phi\f$ of a \c Cmp .
* Note that in the compactified external domain (CED), it computes
* \f$1/(u\sin\theta) \partial/ \partial \phi =
* r/\sin\theta \partial/ \partial \phi\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void srstdsdp(const Cmp& ci, Cmp& resu) const = 0 ;
/** Computes \f$\partial/ \partial xi\f$ of a \c Scalar .
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdxi(const Scalar& uu, Scalar& resu) const = 0 ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar .
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdr(const Scalar& uu, Scalar& resu) const = 0 ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar if the description is affine and
* \f$\partial/ \partial \ln r\f$ if it is logarithmic.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdradial(const Scalar& uu, Scalar& resu) const = 0 ;
/** Computes \f$1/r \partial/ \partial \theta\f$ of a \c Scalar .
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void srdsdt(const Scalar& uu, Scalar& resu) const = 0 ;
/** Computes \f$1/(r\sin\theta) \partial/ \partial \phi\f$ of a \c Scalar .
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void srstdsdp(const Scalar& uu, Scalar& resu) const = 0 ;
/** Computes \f$\partial/ \partial \theta\f$ of a \c Scalar .
* @param uu [input] scalar field
* @param resu [output] derivative of \c uu
*/
virtual void dsdt(const Scalar& uu, Scalar& resu) const = 0 ;
/** Computes \f$1/\sin\theta \partial/ \partial \varphi\f$ of a \c Scalar .
* @param uu [input] scalar field
* @param resu [output] derivative of \c uu
*/
virtual void stdsdp(const Scalar& uu, Scalar& resu) const = 0 ;
/** Computes the Laplacian of a scalar field.
* @param uu [input] Scalar field \e u (represented as a \c Scalar )
* the Laplacian \f$\Delta u\f$ of which is to be computed
* @param zec_mult_r [input] Determines the quantity computed in
* the compactified external domain (CED) : \\
* zec_mult_r = 0 : \f$\Delta u\f$ \\
* zec_mult_r = 2 : \f$r^2 \, \Delta u\f$ \\
* zec_mult_r = 4 (default) : \f$r^4 \, \Delta u\f$
* @param lap [output] Laplacian of \e u
*/
virtual void laplacien(const Scalar& uu, int zec_mult_r,
Scalar& lap) const = 0 ;
/// Computes the Laplacian of a scalar field (\c Cmp version).
virtual void laplacien(const Cmp& uu, int zec_mult_r,
Cmp& lap) const = 0 ;
/** Computes the angular Laplacian of a scalar field.
* @param uu [input] Scalar field \e u (represented as a \c Scalar )
* the Laplacian \f$\Delta u\f$ of which is to be computed
* @param lap [output] Angular Laplacian of \e u (see documentation
* of \c Scalar
*/
virtual void lapang(const Scalar& uu, Scalar& lap) const = 0 ;
/** Computes the radial primitive which vanishes for \f$r\to \infty\f$.
* i.e. the function
* \f$ F(r,\theta,\varphi) = \int_r^\infty f(r',\theta,\varphi) \, dr' \f$
*
* @param uu [input] function \e f (must have a \c dzpuis = 2)
* @param resu [input] function \e F
* @param null_infty if true (default), the primitive is null
* at infinity (or on the grid boundary). \e F is null at the
* center otherwise
*/
virtual void primr(const Scalar& uu, Scalar& resu,
bool null_infty) const = 0 ;
// Various linear operators
// ------------------------
public:
/** Multiplication by \e r of a \c Scalar , the \c dzpuis
* of \c uu is not changed.
*/
virtual void mult_r(Scalar& uu) const = 0 ;
/** Multiplication by \e r of a \c Cmp . In the CED,
* there is only a decrement of \c dzpuis
*/
virtual void mult_r(Cmp& ci) const = 0 ;
/** Multiplication by \e r (in the compactified external domain only)
* of a \c Scalar
*/
virtual void mult_r_zec(Scalar& ) const = 0 ;
/** Multiplication by \f$r\sin\theta\f$ of a \c Scalar
*/
virtual void mult_rsint(Scalar& ) const = 0 ;
/** Division by \f$r\sin\theta\f$ of a \c Scalar
*/
virtual void div_rsint(Scalar& ) const = 0 ;
/** Division by \e r of a \c Scalar
*/
virtual void div_r(Scalar& ) const = 0 ;
/** Division by \e r (in the compactified external domain only)
* of a \c Scalar
*/
virtual void div_r_zec(Scalar& ) const = 0 ;
/** Multiplication by \f$\cos\theta\f$ of a \c Scalar
*/
virtual void mult_cost(Scalar& ) const = 0 ;
/** Division by \f$\cos\theta\f$ of a \c Scalar
*/
virtual void div_cost(Scalar& ) const = 0 ;
/** Multiplication by \f$\sin\theta\f$ of a \c Scalar
*/
virtual void mult_sint(Scalar& ) const = 0 ;
/** Division by \f$\sin\theta\f$ of a \c Scalar
*/
virtual void div_sint(Scalar& ) const = 0 ;
/** Division by \f$\tan\theta\f$ of a \c Scalar
*/
virtual void div_tant(Scalar& ) const = 0 ;
/** Computes the Cartesian x component (with respect to
* \c bvect_cart ) of a vector given
* by its spherical components with respect to \c bvect_spher .
*
* @param v_r [input] \e r -component of the vector
* @param v_theta [input] \f$\theta\f$-component of the vector
* @param v_phi [input] \f$\phi\f$-component of the vector
* @param v_x [output] x-component of the vector
*/
virtual void comp_x_from_spherical(const Scalar& v_r, const Scalar& v_theta,
const Scalar& v_phi, Scalar& v_x) const = 0 ;
/// \c Cmp version
virtual void comp_x_from_spherical(const Cmp& v_r, const Cmp& v_theta,
const Cmp& v_phi, Cmp& v_x) const = 0 ;
/** Computes the Cartesian y component (with respect to
* \c bvect_cart ) of a vector given
* by its spherical components with respect to \c bvect_spher .
*
* @param v_r [input] \e r -component of the vector
* @param v_theta [input] \f$\theta\f$-component of the vector
* @param v_phi [input] \f$\phi\f$-component of the vector
* @param v_y [output] y-component of the vector
*/
virtual void comp_y_from_spherical(const Scalar& v_r, const Scalar& v_theta,
const Scalar& v_phi, Scalar& v_y) const = 0 ;
/// \c Cmp version
virtual void comp_y_from_spherical(const Cmp& v_r, const Cmp& v_theta,
const Cmp& v_phi, Cmp& v_y) const = 0 ;
/** Computes the Cartesian z component (with respect to
* \c bvect_cart ) of a vector given
* by its spherical components with respect to \c bvect_spher .
*
* @param v_r [input] \e r -component of the vector
* @param v_theta [input] \f$\theta\f$-component of the vector
* @param v_z [output] z-component of the vector
*/
virtual void comp_z_from_spherical(const Scalar& v_r, const Scalar& v_theta,
Scalar& v_z) const = 0 ;
/// \c Cmp version
virtual void comp_z_from_spherical(const Cmp& v_r, const Cmp& v_theta,
Cmp& v_z) const = 0 ;
/** Computes the Spherical r component (with respect to
* \c bvect_spher ) of a vector given
* by its cartesian components with respect to \c bvect_cart .
*
* @param v_x [input] x-component of the vector
* @param v_y [input] y-component of the vector
* @param v_z [input] z-component of the vector
* @param v_r [output] \e r -component of the vector
*/
virtual void comp_r_from_cartesian(const Scalar& v_x, const Scalar& v_y,
const Scalar& v_z, Scalar& v_r) const = 0 ;
/// \c Cmp version
virtual void comp_r_from_cartesian(const Cmp& v_x, const Cmp& v_y,
const Cmp& v_z, Cmp& v_r) const = 0 ;
/** Computes the Spherical \f$\theta\f$ component (with respect to
* \c bvect_spher ) of a vector given
* by its cartesian components with respect to \c bvect_cart .
*
* @param v_x [input] x-component of the vector
* @param v_y [input] y-component of the vector
* @param v_z [input] z-component of the vector
* @param v_t [output] \f$\theta\f$-component of the vector
*/
virtual void comp_t_from_cartesian(const Scalar& v_x, const Scalar& v_y,
const Scalar& v_z, Scalar& v_t) const = 0 ;
/// \c Cmp version
virtual void comp_t_from_cartesian(const Cmp& v_x, const Cmp& v_y,
const Cmp& v_z, Cmp& v_t) const = 0 ;
/** Computes the Spherical \f$\phi\f$ component (with respect to
* \c bvect_spher ) of a vector given
* by its cartesian components with respect to \c bvect_cart .
*
* @param v_x [input] x-component of the vector
* @param v_y [input] y-component of the vector
* @param v_p [output] \f$\phi\f$-component of the vector
*/
virtual void comp_p_from_cartesian(const Scalar& v_x, const Scalar& v_y,
Scalar& v_p) const = 0 ;
/// \c Cmp version
virtual void comp_p_from_cartesian(const Cmp& v_x, const Cmp& v_y,
Cmp& v_p) const = 0 ;
/** Decreases by 1 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void dec_dzpuis(Scalar& ) const = 0 ;
/** Decreases by 2 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void dec2_dzpuis(Scalar& ) const = 0 ;
/** Increases by 1 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void inc_dzpuis(Scalar& ) const = 0 ;
/** Increases by 2 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void inc2_dzpuis(Scalar& ) const = 0 ;
/** Computes the integral over all space of a \c Cmp .
* The computed quantity is
* \f$\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi\f$.
* The routine allocates a \c Tbl (size: \c mg->nzone ) to store
* the result (partial integral) in each domain and returns a pointer
* to it.
*/
virtual Tbl* integrale(const Cmp&) const = 0 ;
// PDE resolution :
// --------------
public:
/** Computes the solution of a scalar Poisson equation.
*
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* \f$\Delta u = \sigma\f$.
* @param par [input/output] possible parameters to control the
* resolution of the Poisson equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param uu [input/output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
virtual void poisson(const Cmp& source, Param& par, Cmp& uu) const = 0 ;
/** Computes the solution of a scalar Poisson equationwith a Tau method.
*
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* \f$\Delta u = \sigma\f$.
* @param par [input/output] possible parameters to control the
* resolution of the Poisson equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param uu [input/output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
virtual void poisson_tau(const Cmp& source, Param& par, Cmp& uu) const = 0 ;
virtual void poisson_falloff(const Cmp& source, Param& par, Cmp& uu,
int k_falloff) const = 0 ;
virtual void poisson_ylm(const Cmp& source, Param& par, Cmp& pot,
int nylm, double* intvec) const = 0 ;
/** Computes the solution of a scalar Poisson equation.
* The regularized source
*
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* \f$\Delta u = \sigma\f$.
* @param k_div [input] regularization degree of the procedure
* @param nzet [input] number of domains covering the star
* @param unsgam1 [input] parameter \f$1/(\gamma-1)\f$ where \f$\gamma\f$
* denotes the adiabatic index.
* @param par [input/output] possible parameters to control the
* resolution of the Poisson equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param uu [input/output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
* @param uu_regu [output] solution of the regular part of
* the source.
* @param uu_div [output] solution of the diverging part of
* the source.
* @param duu_div [output] derivative of the diverging potential
* @param source_regu [output] regularized source
* @param source_div [output] diverging part of the source
*/
virtual void poisson_regular(const Cmp& source, int k_div, int nzet,
double unsgam1, Param& par, Cmp& uu,
Cmp& uu_regu, Cmp& uu_div,
Tenseur& duu_div, Cmp& source_regu,
Cmp& source_div) const = 0 ;
/** Resolution of the elliptic equation
* \f$ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma\f$
* in the case where the stellar interior is covered by a single domain.
*
* @param source [input] source \f$\sigma\f$ of the above equation
* @param aa [input] factor \e a in the above equation
* @param bb [input] vector \e \b b in the above equation
* @param par [input/output] possible parameters to control the
* resolution of the equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param psi [input/output] solution \f$\psi\f$ which satisfies
* \f$\psi(0)=0\f$.
*/
virtual void poisson_compact(const Cmp& source, const Cmp& aa,
const Tenseur& bb, const Param& par,
Cmp& psi) const = 0 ;
/** Resolution of the elliptic equation
* \f$ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma\f$
* in the case of a multidomain stellar interior.
*
* @param nzet [input] number of domains covering the stellar interior
* @param source [input] source \f$\sigma\f$ of the above equation
* @param aa [input] factor \e a in the above equation
* @param bb [input] vector \e \b b in the above equation
* @param par [input/output] possible parameters to control the
* resolution of the equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param psi [input/output] solution \f$\psi\f$ which satisfies
* \f$\psi(0)=0\f$.
*/
virtual void poisson_compact(int nzet, const Cmp& source, const Cmp& aa,
const Tenseur& bb, const Param& par,
Cmp& psi) const = 0 ;
/** Computes the solution of the generalized angular Poisson equation.
* The generalized angular Poisson equation is
* \f$\Delta_{\theta\varphi} u + \lambda u = \sigma\f$,
* where \f$\Delta_{\theta\varphi} u := \frac{\partial^2 u}
* {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial u}
* {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 u}
* {\partial \varphi^2}\f$.
*
* @param source [input] source \f$\sigma\f$ of the equation
* \f$\Delta_{\theta\varphi} u + \lambda u = \sigma\f$.
* @param par [input/output] possible parameters to control the
* resolution of the Poisson equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param uu [input/output] solution \e u
* @param lambda [input] coefficient \f$\lambda\f$ in the above equation
* (default value = 0)
*/
virtual void poisson_angu(const Scalar& source, Param& par,
Scalar& uu, double lambda=0) const = 0 ;
public:
/**
* Function intended to be used by \c Map::poisson_vect
* and \c Map::poisson_vect_oohara . It constructs the sets of
* parameters used for each scalar Poisson equation from the one for
* the vectorial one.
*
* @param para [input] : the \c Param used for the resolution of
* the vectorial Poisson equation : \\
* \c para.int() maximum number of iteration.\\
* \c para.double(0) relaxation parameter.\\
* \c para.double(1) required precision. \\
* \c para.tenseur_mod() source of the vectorial part at the previous
* step.\\
* \c para.cmp_mod() source of the scalar part at the previous
* step.
*
* @param i [input] number of the scalar Poisson equation that is being
* solved (values from 0 to 2 for the componants of the vectorial part
* and 3 for the scalar one).
*
* @return the pointer on the parameter set used for solving the
* scalar Poisson equation labelled by \e i .
*/
virtual Param* donne_para_poisson_vect (Param& para, int i) const = 0;
/**
* Computes the solution of a Poisson equation from the domain
* \c num_front+1 .
* imposing a boundary condition at the boundary between the domains
* \c num_front and \c num_front+1 .
*
* @param source [input] : source of the equation.
* @param limite [input] : \c limite[num_front] contains the angular
* function being the boudary condition.
* @param raccord [input] : 1 for the Dirichlet problem and 2 for
* the Neumann one and 3 for Dirichlet-Neumann.
* @param num_front [input] : index of the boudary at which the boundary
* condition has to be imposed.
* @param pot [output] : result.
* @param fact_dir [input] : Valeur by which we multiply the quantity
* we solve. (in the case of Dirichlet-Neumann boundary condition.)
* @param fact_neu [input] : Valeur by which we multiply the radial
* derivative of the quantity we solve. (in the case of
* Dirichlet-Neumann boundary condition.)
*/
virtual void poisson_frontiere (const Cmp& source,const Valeur& limite,
int raccord, int num_front, Cmp& pot,
double = 0., double = 0.) const = 0 ;
virtual void poisson_frontiere_double (const Cmp& source, const Valeur& lim_func,
const Valeur& lim_der, int num_zone, Cmp& pot) const = 0 ;
/**
* Computes the solution of a Poisson equation in the shell,
* imposing a boundary condition at the surface of the star
*
* @param source [input] : source of the equation.
* @param limite [input] : \c limite[num_front] contains the angular
* function being the boudary condition.
* @param par [input] : parameters of the computation.
* @param pot [output] : result.
*/
virtual void poisson_interne (const Cmp& source, const Valeur& limite,
Param& par, Cmp& pot) const = 0 ;
/** Computes the solution of a 2-D Poisson equation.
* The 2-D Poisson equation writes
* \f[
* {\partial^2 u\over\partial r^2} +
* {1\over r} {\partial u \over \partial r} +
* {1\over r^2} {\partial^2 u\over\partial \theta^2} =
* \sigma \ .
* \f]
*
* @param source_mat [input] Compactly supported part of
* the source \f$\sigma\f$ of the 2-D Poisson equation (typically
* matter terms)
* @param source_quad [input] Non-compactly supported part of
* the source \f$\sigma\f$ of the 2-D Poisson equation (typically
* quadratic terms)
* @param par [input/output] possible parameters to control the
* resolution of the Poisson equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param uu [input/output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
virtual void poisson2d(const Cmp& source_mat, const Cmp& source_quad,
Param& par, Cmp& uu) const = 0 ;
/** Performs one time-step integration of the d'Alembert scalar equation
* @param par [input/output] possible parameters to control the
* resolution of the wave equation. See the actual implementation
* in the derived class of \c Map for documentation. Note that,
* at least, param must contain the time step as first \c double
* parameter.
* @param fJp1 [output] solution \f$f^{J+1}\f$ at time \e J+1
* with boundary conditions of outgoing radiation (not exact!)
* @param fJ [input] solution \f$f^J\f$ at time \e J
* @param fJm1 [input] solution \f$f^{J-1}\f$ at time \e J-1
* @param source [input] source \f$\sigma\f$ of the d'Alembert equation
* \f$\diamond u = \sigma\f$.
*/
virtual void dalembert(Param& par, Scalar& fJp1, const Scalar& fJ,
const Scalar& fJm1, const Scalar& source) const = 0 ;
// Friend functions :
// ----------------
friend ostream& operator<<(ostream& , const Map& ) ; ///< Operator <<
};
ostream& operator<<(ostream& , const Map& ) ;
//------------------------------------//
// class Map_radial //
//------------------------------------//
/**
* Base class for pure radial mappings. \ingroup (map)
*
* A pure radial mapping is a mapping of the type \f$r=R(\xi, \theta', \phi')\f$,
* \f$\theta=\theta'\f$, \f$\phi=\phi'\f$.
* The class \c Map_radial is an abstract class. Effective implementations
* of radial mapping are performed by the derived class \c Map_af and
* \c Map_et .
*
*
*/
class Map_radial : public Map {
// Data :
// ----
// 0th order derivatives of the mapping
// - - - - - - - - - - - - - - - - - -
public:
/**
* \f$\xi/R\f$ in the nucleus; \\
* \e 1/R in the non-compactified shells; \\
* \f$(\xi-1)/U\f$ in the compactified outer domain.
*/
Coord xsr ;
// 1st order derivatives of the mapping
// - - - - - - - - - - - - - - - - - -
public:
/**
* \f$1/(\partial R/\partial\xi) = \partial \xi /\partial r\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-1/(\partial U/\partial\xi) = - \partial \xi /\partial u\f$ in the
* compactified outer domain.
*/
Coord dxdr ;
/**
* \f$\partial R/\partial\theta'\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-\partial U/\partial\theta'\f$ in the
* compactified external domain (CED).
*/
Coord drdt ;
/**
* \f${1\over\sin\theta} \partial R/\partial\varphi'\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-{1\over\sin\theta}\partial U/\partial\varphi'\f$ in the
* compactified external domain (CED).
*/
Coord stdrdp ;
/**
* \f$1/R \times (\partial R/\partial\theta')\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-1/U \times (\partial U/\partial\theta)\f$ in the
* compactified outer domain.
*/
Coord srdrdt ;
/**
* \f$1/(R\sin\theta) \times (\partial R/\partial\varphi')\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-1/(U\sin\theta) \times (\partial U/\partial\varphi')\f$ in the
* compactified outer domain.
*/
Coord srstdrdp ;
/**
* \f$1/R^2 \times (\partial R/\partial\theta')\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-1/U^2 \times (\partial U/\partial\theta')\f$ in the
* compactified outer domain.
*/
Coord sr2drdt ;
/**
* \f$1/(R^2\sin\theta) \times (\partial R/\partial\varphi')\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-1/(U^2\sin\theta) \times (\partial U/\partial\varphi')\f$ in the
* compactified outer domain.
*/
Coord sr2stdrdp ;
// 2nd order derivatives of the mapping
// - - - - - - - - - - - - - - - - - -
public:
/**
* \f$\partial^2 R/\partial\xi^2\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-\partial^2 U/\partial\xi^2 \f$ in the
* compactified outer domain.
*/
Coord d2rdx2 ;
/**
* \f$1/R^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta'
* (\sin\theta \partial R /\partial\theta') + 1/\sin^2\theta
* \partial^2 R /\partial{\varphi'}^2] \f$ in the nucleus
* and in the non-compactified shells; \\
* \f$- 1/U^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta'
* (\sin\theta \partial U /\partial\theta') + 1/\sin^2\theta
* \partial^2 U /\partial{\varphi'}^2] \f$ in the
* compactified outer domain.
*/
Coord lapr_tp ;
/**
* \f$\partial^2 R/\partial\xi\partial\theta'\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-\partial^2 U/\partial\xi\partial\theta'\f$ in the
* compactified outer domain.
*/
Coord d2rdtdx ;
/**
* \f$1/\sin\theta \times \partial^2 R/\partial\xi\partial\varphi'\f$
* in the nucleus and in the non-compactified shells; \\
* \f$-1/\sin\theta \times \partial^2 U/\partial\xi\partial\varphi' \f$
* in the compactified outer domain.
*/
Coord sstd2rdpdx ;
/**
* \f$1/R^2 \partial^2 R/\partial{\theta'}^2\f$ in the nucleus
* and in the non-compactified shells; \\
* \f$-1/U^2 \partial^2 U/\partial{\theta'}^2\f$ in the
* compactified outer domain.
*/
Coord sr2d2rdt2 ;
// Constructors, destructor :
// ------------------------
protected:
/// Constructor from a grid (protected to make \c Map_radial an abstract class)
Map_radial(const Mg3d& mgrid ) ;
Map_radial(const Map_radial& mp) ; ///< Copy constructor
Map_radial (const Mg3d&, FILE* ) ; ///< Constructor from a file (see \c sauve(FILE* ) )
public:
virtual ~Map_radial() ; ///< Destructor
// Memory management
// -----------------
protected:
virtual void reset_coord() ; ///< Resets all the member \c Coords
// Modification of the mapping
// ---------------------------
public:
/// Assignment to an affine mapping.
virtual void operator=(const Map_af& ) = 0 ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
// Extraction of information
// -------------------------
/** Returns the value of the radial coordinate \e r for a given
* \f$\xi\f$ and a given collocation point in \f$(\theta', \phi')\f$
* in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param j [input] index of the collocation point in \f$\theta'\f$
* @param k [input] index of the collocation point in \f$\phi'\f$
* @return value of \f$r=R_l(\xi, {\theta'}_j, {\phi'}_k)\f$
*/
virtual double val_r_jk(int l, double xi, int j, int k) const = 0 ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point of arbitrary \e r but collocation values of \f$(\theta, \phi)\f$
* @param rr [input] value of \e r
* @param j [input] index of the collocation point in \f$\theta\f$
* @param k [input] index of the collocation point in \f$\phi\f$
* @param par [input/output] parameters to control the
* accuracy of the computation
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx_jk(double rr, int j, int k, const Param& par,
int& l, double& xi) const = 0 ;
/// Comparison operator (egality)
virtual bool operator==(const Map& ) const = 0;
// Values of a Cmp at the new grid points
// --------------------------------------
/** Recomputes the values of a \c Cmp at the collocation points
* after a change in the mapping.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Cmp previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Cmp
* at the grid points defined by \c *this.
*/
virtual void reevaluate(const Map* mp_prev, int nzet, Cmp& uu) const ;
/** Recomputes the values of a \c Cmp at the collocation points
* after a change in the mapping.
* Case where the \c Cmp is symmetric with respect to the plane y=0.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Cmp previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Cmp
* at the grid points defined by \c *this.
*/
virtual void reevaluate_symy(const Map* mp_prev, int nzet, Cmp& uu)
const ;
/** Recomputes the values of a \c Scalar at the collocation points
* after a change in the mapping.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Scalar previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Scalar
* at the grid points defined by \c *this.
*/
virtual void reevaluate(const Map* mp_prev, int nzet, Scalar& uu) const ;
/** Recomputes the values of a \c Scalar at the collocation points
* after a change in the mapping.
* Case where the \c Scalar is symmetric with respect to the plane y=0.
* @param mp_prev [input] Previous value of the mapping.
* @param nzet [input] Number of domains where the computation
* must be done: the computation is performed for the domains
* of index \f$0\le {\tt l} \le {\tt nzet-1}\f$; \c uu is set
* to zero in the other domains.
* @param uu [input/output] input : \c Scalar previously computed on
* the mapping \c *mp_prev ; ouput :
* values of (logically) the same \c Scalar
* at the grid points defined by \c *this.
*/
virtual void reevaluate_symy(const Map* mp_prev, int nzet, Scalar& uu)
const ;
// Various linear operators
// ------------------------
public:
/** Multiplication by \e r of a \c Scalar, the \c dzpuis
* of \c uu is not changed.
*/
virtual void mult_r(Scalar& uu) const ;
/** Multiplication by \e r of a \c Cmp. In the CED,
* there is only a decrement of \c dzpuis
*/
virtual void mult_r(Cmp& ci) const ;
/**
* Multiplication by \e r (in the compactified external domain only)
* of a \c Scalar
*/
virtual void mult_r_zec(Scalar& ) const ;
/** Multiplication by \f$r\sin\theta\f$ of a \c Scalar
*/
virtual void mult_rsint(Scalar& ) const ;
/** Division by \f$r\sin\theta\f$ of a \c Scalar
*/
virtual void div_rsint(Scalar& ) const ;
/** Division by \e r of a \c Scalar
*/
virtual void div_r(Scalar& ) const ;
/** Division by \e r (in the compactified external domain only)
* of a \c Scalar
*/
virtual void div_r_zec(Scalar& ) const ;
/** Multiplication by \f$\cos\theta\f$ of a \c Scalar
*/
virtual void mult_cost(Scalar& ) const ;
/** Division by \f$\cos\theta\f$ of a \c Scalar
*/
virtual void div_cost(Scalar& ) const ;
/** Multiplication by \f$\sin\theta\f$ of a \c Scalar
*/
virtual void mult_sint(Scalar& ) const ;
/** Division by \f$\sin\theta\f$ of a \c Scalar
*/
virtual void div_sint(Scalar& ) const ;
/** Division by \f$\tan\theta\f$ of a \c Scalar
*/
virtual void div_tant(Scalar& ) const ;
/** Computes the Cartesian x component (with respect to
* \c bvect_cart) of a vector given
* by its spherical components with respect to \c bvect_spher.
*
* @param v_r [input] \e r -component of the vector
* @param v_theta [input] \f$\theta\f$-component of the vector
* @param v_phi [input] \f$\phi\f$-component of the vector
* @param v_x [output] x-component of the vector
*/
virtual void comp_x_from_spherical(const Scalar& v_r, const Scalar& v_theta,
const Scalar& v_phi, Scalar& v_x) const ;
/// \c Cmp version
virtual void comp_x_from_spherical(const Cmp& v_r, const Cmp& v_theta,
const Cmp& v_phi, Cmp& v_x) const ;
/** Computes the Cartesian y component (with respect to
* \c bvect_cart ) of a vector given
* by its spherical components with respect to \c bvect_spher .
*
* @param v_r [input] \e r -component of the vector
* @param v_theta [input] \f$\theta\f$-component of the vector
* @param v_phi [input] \f$\phi\f$-component of the vector
* @param v_y [output] y-component of the vector
*/
virtual void comp_y_from_spherical(const Scalar& v_r, const Scalar& v_theta,
const Scalar& v_phi, Scalar& v_y) const ;
/// \c Cmp version
virtual void comp_y_from_spherical(const Cmp& v_r, const Cmp& v_theta,
const Cmp& v_phi, Cmp& v_y) const ;
/** Computes the Cartesian z component (with respect to
* \c bvect_cart ) of a vector given
* by its spherical components with respect to \c bvect_spher .
*
* @param v_r [input] \e r -component of the vector
* @param v_theta [input] \f$\theta\f$-component of the vector
* @param v_z [output] z-component of the vector
*/
virtual void comp_z_from_spherical(const Scalar& v_r, const Scalar& v_theta,
Scalar& v_z) const ;
/// \c Cmp version
virtual void comp_z_from_spherical(const Cmp& v_r, const Cmp& v_theta,
Cmp& v_z) const ;
/** Computes the Spherical r component (with respect to
* \c bvect_spher ) of a vector given
* by its cartesian components with respect to \c bvect_cart .
*
* @param v_x [input] x-component of the vector
* @param v_y [input] y-component of the vector
* @param v_z [input] z-component of the vector
* @param v_r [output] \e r -component of the vector
*/
virtual void comp_r_from_cartesian(const Scalar& v_x, const Scalar& v_y,
const Scalar& v_z, Scalar& v_r) const ;
/// \c Cmp version
virtual void comp_r_from_cartesian(const Cmp& v_x, const Cmp& v_y,
const Cmp& v_z, Cmp& v_r) const ;
/** Computes the Spherical \f$\theta\f$ component (with respect to
* \c bvect_spher ) of a vector given
* by its cartesian components with respect to \c bvect_cart .
*
* @param v_x [input] x-component of the vector
* @param v_y [input] y-component of the vector
* @param v_z [input] z-component of the vector
* @param v_t [output] \f$\theta\f$-component of the vector
*/
virtual void comp_t_from_cartesian(const Scalar& v_x, const Scalar& v_y,
const Scalar& v_z, Scalar& v_t) const ;
/// \c Cmp version
virtual void comp_t_from_cartesian(const Cmp& v_x, const Cmp& v_y,
const Cmp& v_z, Cmp& v_t) const ;
/** Computes the Spherical \f$\phi\f$ component (with respect to
* \c bvect_spher ) of a vector given
* by its cartesian components with respect to \c bvect_cart .
*
* @param v_x [input] x-component of the vector
* @param v_y [input] y-component of the vector
* @param v_p [output] \f$\phi\f$-component of the vector
*/
virtual void comp_p_from_cartesian(const Scalar& v_x, const Scalar& v_y,
Scalar& v_p) const ;
/// \c Cmp version
virtual void comp_p_from_cartesian(const Cmp& v_x, const Cmp& v_y,
Cmp& v_p) const ;
/**
* Decreases by 1 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void dec_dzpuis(Scalar& ) const ;
/**
* Decreases by 2 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void dec2_dzpuis(Scalar& ) const ;
/**
* Increases by 1 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void inc_dzpuis(Scalar& ) const ;
/**
* Increases by 2 the value of \c dzpuis of a \c Scalar
* and changes accordingly its values in the
* compactified external domain (CED).
*/
virtual void inc2_dzpuis(Scalar& ) const ;
// PDE resolution :
// --------------
public:
/** Resolution of the elliptic equation
* \f$ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma\f$
* in the case where the stellar interior is covered by a single domain.
*
* @param source [input] source \f$\sigma\f$ of the above equation
* @param aa [input] factor \e a in the above equation
* @param bb [input] vector \e \b b in the above equation
* @param par [input/output] parameters of the iterative method of
* resolution : \\
* \c par.get_int(0) : [input] maximum number of iterations \\
* \c par.get_double(0) : [input] required precision: the iterative
* method is stopped as soon as the relative difference between
* \f$\psi^J\f$ and \f$\psi^{J-1}\f$ is greater than
* \c par.get_double(0) \\
* \c par.get_double(1) : [input] relaxation parameter \f$\lambda\f$ \\
* \c par.get_int_mod(0) : [output] number of iterations
* actually used to get the solution.
* @param psi [input/output]: input : previously computed value of \f$\psi\f$
* to start the iteration (if nothing is known a priori,
* \c psi must be set to zero);
* output: solution \f$\psi\f$ which satisfies \f$\psi(0)=0\f$.
*/
virtual void poisson_compact(const Cmp& source, const Cmp& aa,
const Tenseur& bb, const Param& par,
Cmp& psi) const ;
/** Resolution of the elliptic equation
* \f$ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma\f$
* in the case of a multidomain stellar interior.
*
* @param nzet [input] number of domains covering the stellar interior
* @param source [input] source \f$\sigma\f$ of the above equation
* @param aa [input] factor \e a in the above equation
* @param bb [input] vector \e \b b in the above equation
* @param par [input/output] possible parameters to control the
* resolution of the equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param psi [input/output] solution \f$\psi\f$ which satisfies
* \f$\psi(0)=0\f$.
*/
virtual void poisson_compact(int nzet, const Cmp& source, const Cmp& aa,
const Tenseur& bb, const Param& par,
Cmp& psi) const ;
};
//------------------------------------//
// class Map_af //
//------------------------------------//
/**
* Affine radial mapping. \ingroup (map)
*
* The affine radial mapping is the simplest one between the grid coordinates
* \f$(\xi, \theta', \phi')\f$ and the physical coordinates \f$(r, \theta, \phi)\f$.
* It is defined by \f$\theta=\theta'\f$, \f$\phi=\phi'\f$ and
* \li \f$r=\alpha \xi + \beta\f$, in non-compactified domains,
* \li \f$ u={1\over r} = \alpha \xi + \beta\f$ in the (usually outermost) compactified
* domain,
* where \f$\alpha\f$ and \f$\beta\f$ are constant in each domain.
*
*
*/
class Map_af : public Map_radial {
// Data :
// ----
private:
/// Array (size: \c mg->nzone ) of the values of \f$\alpha\f$ in each domain
double* alpha ;
/// Array (size: \c mg->nzone ) of the values of \f$\beta\f$ in each domain
double* beta ;
// Constructors, destructor :
// ------------------------
public:
/**
* Standard Constructor
* @param mgrille [input] Multi-domain grid on which the mapping is defined
* @param r_limits [input] Array (size: number of domains + 1) of the
* value of \e r at the boundaries of the various
* domains :
* \li \c r_limits[l] : inner boundary of the
* domain no. \c l
* \li \c r_limits[l+1] : outer boundary of the
* domain no. \c l
*/
Map_af(const Mg3d& mgrille, const double* r_limits) ;
/**
* Standard Constructor with Tbl
* @param mgrille [input] Multi-domain grid on which the mapping is defined
* @param r_limits [input] Array (size: number of domains) of the
* value of \e r at the boundaries of the various
* domains :
* \li \c r_limits[l] : inner boundary of the
* domain no. \c l
* \li \c r_limits[l+1] : outer boundary of the
* domain no. \c l except in the last domain
* The last boundary is set to inifnity if the grid contains a compactified domain.
*/
Map_af(const Mg3d& mgrille, const Tbl& r_limits) ;
Map_af(const Map_af& ) ; ///< Copy constructor
Map_af(const Mg3d&, FILE* ) ; ///< Constructor from a file (see \c sauve(FILE*) )
/** Constructor from a general mapping.
*
* If the input mapping belongs to the class \c Map_af , this
* constructor does the same job as the copy constructor
* \c Map_af(const \c Map_af& \c ) .
*
* If the input mapping belongs to the class \c Map_et , this
* constructor sets in each domain, the values of
* \f$\alpha\f$ and \f$\beta\f$ to those of the \c Map_et .
*
*/
explicit Map_af(const Map& ) ;
virtual ~Map_af() ; ///< Destructor
// Assignment
// ----------
public:
/// Assignment to another affine mapping.
virtual void operator=(const Map_af& ) ;
// Memory management
// -----------------
private:
/// Assignment of the building functions to the member \c Coords
void set_coord() ;
// Extraction of information
// -------------------------
public:
/// Returns the pointer on the array \c alpha
const double* get_alpha() const ;
/// Returns the pointer on the array \c beta
const double* get_beta() const ;
/** Returns the "angular" mapping for the outside of domain \c l_zone.
* Valid only for the class \c Map_af.
*/
virtual const Map_af& mp_angu(int) const ;
/**
* Returns the value of the radial coordinate \e r for a given
* \f$(\xi, \theta', \phi')\f$ in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param theta [input] value of \f$\theta'\f$
* @param pphi [input] value of \f$\phi'\f$
* @return value of \f$r=R_l(\xi, \theta', \phi')\f$
*/
virtual double val_r(int l, double xi, double theta, double pphi) const ;
/**
* Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx(double rr, double theta, double pphi,
int& l, double& xi) const ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param par [] unused by the \c Map_af version
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx(double rr, double theta, double pphi,
const Param& par, int& l, double& xi) const ;
/** Returns the value of the radial coordinate \e r for a given
* \f$\xi\f$ and a given collocation point in \f$(\theta', \phi')\f$
* in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param j [input] index of the collocation point in \f$\theta'\f$
* @param k [input] index of the collocation point in \f$\phi'\f$
* @return value of \f$r=R_l(\xi, {\theta'}_j, {\phi'}_k)\f$
*/
virtual double val_r_jk(int l, double xi, int j, int k) const ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point of arbitrary \e r but collocation values of \f$(\theta, \phi)\f$
* @param rr [input] value of \e r
* @param j [input] index of the collocation point in \f$\theta\f$
* @param k [input] index of the collocation point in \f$\phi\f$
* @param par [] unused by the \c Map_af version
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx_jk(double rr, int j, int k, const Param& par,
int& l, double& xi) const ;
/// Comparison operator (egality)
virtual bool operator==(const Map& ) const ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
private:
virtual ostream& operator>>(ostream &) const ; ///< Operator >>
// Modification of the mapping
// ---------------------------
public:
/** Sets a new radial scale.
* @param lambda [input] factor by which the value of \e r is to
* be multiplied
*/
virtual void homothetie(double lambda) ;
/** Rescales the outer boundary of one domain.
* The inner boundary is unchanged. The inner boundary
* of the next domain is changed to match the new outer
* boundary.
* @param l [input] index of the domain
* @param lambda [input] factor by which the value of
* \f$R(\theta, \varphi)\f$ defining the outer boundary
* of the domain is to be multiplied.
*/
virtual void resize(int l, double lambda) ;
/** Sets a new radial scale at the bondary between the nucleus and the
* first shell.
* @param lambda [input] factor by which the value of \e r is to
* be multiplied
*/
void homothetie_interne(double lambda) ;
/** Adaptation of the mapping to a given scalar field.
*/
virtual void adapt(const Cmp& ent, const Param& par, int nbr=0) ;
/// Modifies the value of \f$\alpha\f$ in domain no. \e l
void set_alpha(double alpha0, int l) ;
/// Modifies the value of \f$\beta\f$ in domain no. \e l
void set_beta(double beta0, int l) ;
// Differential operators:
// ----------------------
public:
/** Computes \f$\partial/ \partial \xi\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = \xi^2 \partial/ \partial \xi\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdxi(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = r^2 \partial/ \partial r\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdr(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$1/r \partial/ \partial \theta\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$1/u \partial/ \partial \theta = r \partial/ \partial \theta\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void srdsdt(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$1/(r\sin\theta) \partial/ \partial \phi\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$1/(u\sin\theta) \partial/ \partial \phi =
* r/\sin\theta \partial/ \partial \phi\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void srstdsdp(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdr(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$\partial/ \partial \xi\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdxi(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdradial(const Scalar&, Scalar&) const ;
/** Computes \f$1/r \partial/ \partial \theta\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void srdsdt(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$1/(r\sin\theta) \partial/ \partial \phi\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void srstdsdp(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$\partial/ \partial \theta\f$ of a \c Scalar.
* @param uu [input] scalar field
* @param resu [output] derivative of \c uu
*/
virtual void dsdt(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$1/\sin\theta \partial/ \partial \varphi\f$ of a \c Scalar.
* @param uu [input] scalar field
* @param resu [output] derivative of \c uu
*/
virtual void stdsdp(const Scalar& uu, Scalar& resu) const ;
/** Computes the Laplacian of a scalar field.
* @param uu [input] Scalar field \e u (represented as a \c Scalar )
* the Laplacian \f$\Delta u\f$ of which is to be computed
* @param zec_mult_r [input] Determines the quantity computed in
* the compactified external domain (CED) : \\
* zec_mult_r = 0 : \f$\Delta u\f$ \\
* zec_mult_r = 2 : \f$r^2 \, \Delta u\f$ \\
* zec_mult_r = 4 (default) : \f$r^4 \, \Delta u\f$
* @param lap [output] Laplacian of \e u
*/
virtual void laplacien(const Scalar& uu, int zec_mult_r,
Scalar& lap) const ;
/// Computes the Laplacian of a scalar field (\c Cmp version).
virtual void laplacien(const Cmp& uu, int zec_mult_r,
Cmp& lap) const ;
/** Computes the angular Laplacian of a scalar field.
* @param uu [input] Scalar field \e u (represented as a \c Scalar)
* the Laplacian \f$\Delta u\f$ of which is to be computed
* @param lap [output] Angular Laplacian of \e u (see documentation
* of \c Scalar
*/
virtual void lapang(const Scalar& uu, Scalar& lap) const ;
/** Computes the radial primitive which vanishes for \f$r\to \infty\f$.
* i.e. the function
* \f$ F(r,\theta,\varphi) = \int_r^\infty f(r',\theta,\varphi) \, dr' \f$
*
* @param uu [input] function \e f (must have a \c dzpuis = 2)
* @param resu [input] function \e F
* @param null_infty if true (default), the primitive is null
* at infinity (or on the grid boundary). \e F is null at the
* center otherwise
*/
virtual void primr(const Scalar& uu, Scalar& resu,
bool null_infty) const ;
/** Computes the integral over all space of a \c Cmp.
* The computed quantity is
* \f$\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi\f$.
* The routine allocates a \c Tbl (size: \c mg->nzone ) to store
* the result (partial integral) in each domain and returns a pointer
* to it.
*/
virtual Tbl* integrale(const Cmp&) const ;
// PDE resolution :
// --------------
public:
/** Computes the solution of a scalar Poisson equation.
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* \f$\Delta u = \sigma\f$.
* @param par [] not used by this \c Map_af version.
* @param uu [output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
virtual void poisson(const Cmp& source, Param& par, Cmp& uu) const ;
/** Computes the solution of a scalar Poisson equation using a Tau method.
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* \f$\Delta u = \sigma\f$.
* @param par [] not used by this \c Map_af version.
* @param uu [output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
virtual void poisson_tau(const Cmp& source, Param& par, Cmp& uu) const ;
virtual void poisson_falloff(const Cmp& source, Param& par, Cmp& uu,
int k_falloff) const ;
virtual void poisson_ylm(const Cmp& source, Param& par, Cmp& pot,
int nylm, double* intvec) const ;
/** Computes the solution of a scalar Poisson equation.
* The regularized source
* \f$\sigma_{\rm regu} = \sigma - \sigma_{\rm div}\f$
* is constructed and solved.
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* \f$\Delta u = \sigma\f$.
* @param k_div [input] regularization degree of the procedure
* @param nzet [input] number of domains covering the star
* @param unsgam1 [input] parameter \f$1/(\gamma-1)\f$ where \f$\gamma\f$
* denotes the adiabatic index.
* @param par [] not used by this \c Map_af version.
* @param uu [output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
* @param uu_regu [output] solution of the regular part of
* the source.
* @param uu_div [output] solution of the diverging part of
* the source.
* @param duu_div [output] derivative of the diverging potential
* @param source_regu [output] regularized source
* @param source_div [output] diverging part of the source
*/
virtual void poisson_regular(const Cmp& source, int k_div, int nzet,
double unsgam1, Param& par, Cmp& uu,
Cmp& uu_regu, Cmp& uu_div,
Tenseur& duu_div, Cmp& source_regu,
Cmp& source_div) const ;
/** Computes the solution of the generalized angular Poisson equation.
* The generalized angular Poisson equation is
* \f$\Delta_{\theta\varphi} u + \lambda u = \sigma\f$,
* where \f$\Delta_{\theta\varphi} u := \frac{\partial^2 u}
* {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial u}
* {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 u}
* {\partial \varphi^2}\f$.
*
* @param source [input] source \f$\sigma\f$ of the equation
* \f$\Delta_{\theta\varphi} u + \lambda u = \sigma\f$.
* @param par [input/output] possible parameters to control the
* resolution of the Poisson equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param uu [input/output] solution \e u
* @param lambda [input] coefficient \f$\lambda\f$ in the above equation
* (default value = 0)
*/
virtual void poisson_angu(const Scalar& source, Param& par,
Scalar& uu, double lambda=0) const ;
/**
* Internal function intended to be used by \c Map::poisson_vect
* and \c Map::poisson_vect_oohara . It constructs the sets of
* parameters used for each scalar Poisson equation from the one for
* the vectorial one.
*
* In the case of a \c Map_af the result is not used and the function
* only returns \c & \c par .
*/
virtual Param* donne_para_poisson_vect (Param& par, int i) const ;
/**
* Solver of the Poisson equation with boundary condition for the
* affine mapping case.
*/
virtual void poisson_frontiere (const Cmp&, const Valeur&, int, int, Cmp&, double = 0., double = 0.) const ;
/**
* Solver of the Poisson equation with boundary condition for the
* affine mapping case, cases with boundary conditions of both
* Dirichlet and Neumann type (no condition imposed at infinity).
*/
virtual void poisson_frontiere_double (const Cmp& source, const Valeur& lim_func,
const Valeur& lim_der, int num_zone, Cmp& pot) const ;
/**
* Computes the solution of a Poisson equation in the shell,
* imposing a boundary condition at the surface of the star
*
* @param source [input] : source of the equation.
* @param limite [input] : \c limite[num_front] contains the angular
* function being the boudary condition.
* @param par [input] : parameters of the computation.
* @param pot [output] : result.
*/
virtual void poisson_interne (const Cmp& source, const Valeur& limite,
Param& par, Cmp& pot) const ;
/**
* Performs the surface integration of \c ci on the sphere of
* radius \c rayon .
*/
double integrale_surface (const Cmp& ci, double rayon) const ;
/**
* Performs the surface integration of \c ci on the sphere of
* radius \c rayon .
*/
double integrale_surface (const Scalar& ci, double rayon) const ;
double integrale_surface_falloff (const Cmp& ci) const ;
/**
* Performs the surface integration of \c ci at infinity.
* \c ci must have \c dzpuis =2.
*/
double integrale_surface_infini (const Cmp& ci) const ;
/**
* Performs the surface integration of \c ci at infinity.
* \c ci must have \c dzpuis =2.
*/
double integrale_surface_infini (const Scalar& ci) const ;
/**
* General elliptic solver. The field is zero at infinity.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
**/
void sol_elliptic (Param_elliptic& params,
const Scalar& so, Scalar& uu) const ;
/**
* General elliptic solver including inner boundary conditions.
* The field is zero at infinity.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
* @param bound [input] : the boundary condition
* @param fact_dir : 1 Dirchlet condition, 0 Neumann condition
* @param fact_neu : 0 Dirchlet condition, 1 Neumann condition
**/
void sol_elliptic_boundary (Param_elliptic& params,
const Scalar& so, Scalar& uu, const Mtbl_cf& bound,
double fact_dir, double fact_neu ) const ;
/**
* General elliptic solver including inner boundary conditions, with
* boundary given as a Scalar on mono-domain angular grid
**/
void sol_elliptic_boundary (Param_elliptic& params,
const Scalar& so, Scalar& uu, const Scalar& bound,
double fact_dir, double fact_neu ) const ;
/**
* General elliptic solver.
* The equation is not solved in the compactified domain.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
* @param val [input] : value at the last shell.
**/
void sol_elliptic_no_zec (Param_elliptic& params,
const Scalar& so, Scalar& uu, double val) const ;
/**
* General elliptic solver.
* The equation is solved only in the compactified domain.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
* @param val [input] : value at the inner boundary.
**/
void sol_elliptic_only_zec (Param_elliptic& params,
const Scalar& so, Scalar& uu, double val) const ;
/**
* General elliptic solver.
* The equation is not solved in the compactified domain and the
* matching is done with an homogeneous solution.
**/
void sol_elliptic_sin_zec (Param_elliptic& params,
const Scalar& so, Scalar& uu,
double* coefs, double*) const ;
/**
* General elliptic solver fixing the derivative at the origin
* and relaxing the continuity of the first derivative at the
* boundary between the nucleus and the first shell.
*
* @param val [input] : valeur of the derivative.
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
**/
void sol_elliptic_fixe_der_zero (double val,
Param_elliptic& params,
const Scalar& so, Scalar& uu) const ;
/** Computes the solution of a 2-D Poisson equation.
* The 2-D Poisson equation writes
* \f[
* {\partial^2 u\over\partial r^2} +
* {1\over r} {\partial u \over \partial r} +
* {1\over r^2} {\partial^2 u\over\partial \theta^2} =
* \sigma \ .
* \f]
*
* @param source_mat [input] Compactly supported part of
* the source \f$\sigma\f$ of the 2-D Poisson equation (typically
* matter terms)
* @param source_quad [input] Non-compactly supported part of
* the source \f$\sigma\f$ of the 2-D Poisson equation (typically
* quadratic terms)
* @param par [output] Parameter which contains the constant
* \f$\lambda\f$ used to fulfill the virial
* identity GRV2 : \\
* \c par.get_double_mod(0) : [output] constant \c lambda
* such that the source of the equation effectively solved
* is \c source_mat + \c lambda * \c source_quad .
* @param uu [input/output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
virtual void poisson2d(const Cmp& source_mat, const Cmp& source_quad,
Param& par, Cmp& uu) const ;
/**
* General elliptic solver in a 2D case. The field is zero at infinity.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
**/
void sol_elliptic_2d(Param_elliptic&,
const Scalar&, Scalar&) const ;
/**
* General elliptic solver in a pseudo 1d case. The field is zero at infinity.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
**/
void sol_elliptic_pseudo_1d(Param_elliptic&,
const Scalar&, Scalar&) const ;
/** Performs one time-step integration of the d'Alembert scalar equation
* @param par [input/output] possible parameters to control the
* resolution of the d'Alembert equation: \\
* \c par.get_double(0) : [input] the time step \e dt ,\\
* \c par.get_int(0) : [input] the type of boundary conditions
* set at the outer boundary (0 : reflexion, 1 : Sommerfeld
* outgoing wave, valid only for \e l=0 components, 2 : Bayliss
* & Turkel outgoing wave, valid for \e l=0, 1, 2 components)\\
* \c par.get_int_mod(0) : [input/output] set to 0 at first
* call, is used as a working flag after (must not be modified after
* first call)\\
* \c par.get_int(1) : [input] (optional) if present, a shift of
* -1 is done in the multipolar spectrum in terms of \f$\ell\f$.
* The value of this variable gives the minimal value of (the shifted)
* \f$\ell\f$ for which the wave equation is solved.\\
* \c par.get_tensor_mod(0) : [input] (optional) if the wave
* equation is on a curved space-time, this is the potential in front
* of the Laplace operator. It has to be updated at every time-step
* (for a potential depending on time).\\
* Note: there are many other working objects attached to this
* \c Param , so one should not modify it.
* @param fJp1 [output] solution \f$f^{J+1}\f$ at time \e J+1
* with boundary conditions defined by \c par.get_int(0)
* @param fJ [input] solution \f$f^J\f$ at time \e J
* @param fJm1 [input] solution \f$f^{J-1}\f$ at time \e J-1
* @param source [input] source \f$\sigma\f$ of the d'Alembert equation
* \f$\diamond u = \sigma\f$.
*/
virtual void dalembert(Param& par, Scalar& fJp1, const Scalar& fJ,
const Scalar& fJm1, const Scalar& source) const ;
// Building functions for the Coord's
// ----------------------------------
friend Mtbl* map_af_fait_r(const Map* ) ;
friend Mtbl* map_af_fait_tet(const Map* ) ;
friend Mtbl* map_af_fait_phi(const Map* ) ;
friend Mtbl* map_af_fait_sint(const Map* ) ;
friend Mtbl* map_af_fait_cost(const Map* ) ;
friend Mtbl* map_af_fait_sinp(const Map* ) ;
friend Mtbl* map_af_fait_cosp(const Map* ) ;
friend Mtbl* map_af_fait_x(const Map* ) ;
friend Mtbl* map_af_fait_y(const Map* ) ;
friend Mtbl* map_af_fait_z(const Map* ) ;
friend Mtbl* map_af_fait_xa(const Map* ) ;
friend Mtbl* map_af_fait_ya(const Map* ) ;
friend Mtbl* map_af_fait_za(const Map* ) ;
friend Mtbl* map_af_fait_xsr(const Map* ) ;
friend Mtbl* map_af_fait_dxdr(const Map* ) ;
friend Mtbl* map_af_fait_drdt(const Map* ) ;
friend Mtbl* map_af_fait_stdrdp(const Map* ) ;
friend Mtbl* map_af_fait_srdrdt(const Map* ) ;
friend Mtbl* map_af_fait_srstdrdp(const Map* ) ;
friend Mtbl* map_af_fait_sr2drdt(const Map* ) ;
friend Mtbl* map_af_fait_sr2stdrdp(const Map* ) ;
friend Mtbl* map_af_fait_d2rdx2(const Map* ) ;
friend Mtbl* map_af_fait_lapr_tp(const Map* ) ;
friend Mtbl* map_af_fait_d2rdtdx(const Map* ) ;
friend Mtbl* map_af_fait_sstd2rdpdx(const Map* ) ;
friend Mtbl* map_af_fait_sr2d2rdt2(const Map* ) ;
};
Mtbl* map_af_fait_r(const Map* ) ;
Mtbl* map_af_fait_tet(const Map* ) ;
Mtbl* map_af_fait_phi(const Map* ) ;
Mtbl* map_af_fait_sint(const Map* ) ;
Mtbl* map_af_fait_cost(const Map* ) ;
Mtbl* map_af_fait_sinp(const Map* ) ;
Mtbl* map_af_fait_cosp(const Map* ) ;
Mtbl* map_af_fait_x(const Map* ) ;
Mtbl* map_af_fait_y(const Map* ) ;
Mtbl* map_af_fait_z(const Map* ) ;
Mtbl* map_af_fait_xa(const Map* ) ;
Mtbl* map_af_fait_ya(const Map* ) ;
Mtbl* map_af_fait_za(const Map* ) ;
Mtbl* map_af_fait_xsr(const Map* ) ;
Mtbl* map_af_fait_dxdr(const Map* ) ;
Mtbl* map_af_fait_drdt(const Map* ) ;
Mtbl* map_af_fait_stdrdp(const Map* ) ;
Mtbl* map_af_fait_srdrdt(const Map* ) ;
Mtbl* map_af_fait_srstdrdp(const Map* ) ;
Mtbl* map_af_fait_sr2drdt(const Map* ) ;
Mtbl* map_af_fait_sr2stdrdp(const Map* ) ;
Mtbl* map_af_fait_d2rdx2(const Map* ) ;
Mtbl* map_af_fait_lapr_tp(const Map* ) ;
Mtbl* map_af_fait_d2rdtdx(const Map* ) ;
Mtbl* map_af_fait_sstd2rdpdx(const Map* ) ;
Mtbl* map_af_fait_sr2d2rdt2(const Map* ) ;
//------------------------------------//
// class Map_et //
//------------------------------------//
/**
* Radial mapping of rather general form. \ingroup (map)
*
* This mapping relates the grid coordinates
* \f$(\xi, \theta', \phi')\f$ and the physical coordinates \f$(r, \theta, \phi)\f$
* in the following manner [see Bonazzola, Gourgoulhon & Marck,
* \e Phys. \e Rev. \e D \b 58 , 104020 (1998) for details]:
* \f$\theta=\theta'\f$, \f$\phi=\phi'\f$ and
* \li \f$r = \alpha [\xi + A(\xi) F(\theta', \phi') + B(\xi) G(\theta', \phi')]
* + \beta\f$ in non-compactified domains,
* \li \f$ u={1\over r} = \alpha [\xi + A(\xi) F(\theta', \phi')] + \beta\f$ in
* the (usually outermost) compactified domain,
* where \f$\alpha\f$ and \f$\beta\f$ are constant in each domain, \f$A(\xi)\f$ and
* \f$B(\xi)\f$ are constant polynomials defined by
* \li \f$A(\xi) = 3 \xi^4 - 2 \xi^6\f$ and
* \f$B(\xi) = (5\xi^3 - 3\xi^5)/2\f$ in the nucleus (innermost domain
* which contains \e r =0);
* \li \f$A(\xi) = (\xi^3 - 3\xi + 2)/4\f$ and
* \f$B(\xi) = (-\xi^3 + 3\xi +2)/4\f$ in the other domains.
* The functions \f$F(\theta', \phi')\f$ and \f$G(\theta', \phi')\f$ depend on the
* domain under consideration and define the boundaries of this domain.
*
*
*/
class Map_et : public Map_radial {
// Data :
// ----
private:
/// Array (size: \c mg->nzone ) of the values of \f$\alpha\f$ in each domain
double* alpha ;
/// Array (size: \c mg->nzone ) of the values of \f$\beta\f$ in each domain
double* beta ;
/** Array (size: \c mg->nzone ) of \c Tbl which stores the
* values of \f$A(\xi)\f$ in each domain
*/
Tbl** aa ;
/** Array (size: \c mg->nzone ) of \c Tbl which stores the
* values of \f$A'(\xi)\f$ in each domain
*/
Tbl** daa ;
/** Array (size: \c mg->nzone ) of \c Tbl which stores the
* values of \f$A''(\xi)\f$ in each domain
*/
Tbl** ddaa ;
/// Values at the \c nr collocation points of \f$A(\xi)/\xi\f$ in the nucleus
Tbl aasx ;
/// Values at the \c nr collocation points of \f$A(\xi)/\xi^2\f$ in the nucleus
Tbl aasx2 ;
/** Values at the \c nr collocation points of \f$A(\xi)/(\xi-1)\f$
* in the outermost compactified domain
*/
Tbl zaasx ;
/** Values at the \c nr collocation points of \f$A(\xi)/(\xi-1)^2\f$
* in the outermost compactified domain
*/
Tbl zaasx2 ;
/** Array (size: \c mg->nzone ) of \c Tbl which stores the
* values of \f$B(\xi)\f$ in each domain
*/
Tbl** bb ;
/** Array (size: \c mg->nzone ) of \c Tbl which stores the
* values of \f$B'(\xi)\f$ in each domain
*/
Tbl** dbb ;
/** Array (size: \c mg->nzone ) of \c Tbl which stores the
* values of \f$B''(\xi)\f$ in each domain
*/
Tbl** ddbb ;
/// Values at the \c nr collocation points of \f$B(\xi)/\xi\f$ in the nucleus
Tbl bbsx ;
/// Values at the \c nr collocation points of \f$B(\xi)/\xi^2\f$ in the nucleus
Tbl bbsx2 ;
/** Values of the function \f$F(\theta', \phi')\f$ at the \c nt*np
* angular collocation points in each domain.
* The \c Valeur \c ff is defined on the multi-grid \c mg->g_angu
* (cf. class \c Mg3d ).
*/
Valeur ff ;
/** Values of the function \f$G(\theta', \phi')\f$ at the \c nt*np
* angular collocation points in each domain.
* The \c Valeur \c gg is defined on the multi-grid \c mg->g_angu
* (cf. class \c Mg3d ).
*/
Valeur gg ;
public:
/** \f$1/(\partial R/\partial \xi) R/\xi\f$ in the nucleus; \\
* \f$1/(\partial R/\partial \xi) R/(\xi + \beta/\alpha)\f$ in the shells; \\
* \f$1/(\partial U/\partial \xi) U/(\xi-1)\f$ in the outermost
* compactified domain.
*/
Coord rsxdxdr ;
/** \f$[ R/ (\alpha \xi + \beta) ]^2 (\partial R/\partial \xi) / \alpha\f$
* in the nucleus and the shells; \\
* \f$\partial U/\partial \xi / \alpha\f$ in the outermost compactified
* domain.
*/
Coord rsx2drdx ;
// Constructors, destructor :
// ------------------------
public:
/**
* Standard Constructor
* @param mgrille [input] Multi-domain grid on which the mapping is defined
* @param r_limits [input] Array (size: number of domains + 1) of the
* value of \e r at the boundaries of the various
* domains :
* \li \c r_limits[l] : inner boundary of the
* domain no. \c l
* \li \c r_limits[l+1] : outer boundary of the
* domain no. \c l
*/
Map_et(const Mg3d& mgrille, const double* r_limits) ;
/**
* Constructor using the equation of the surface of the star.
* @param mgrille [input] Multi-domain grid on which the mapping is defined
* It must contains at least one shell.
* @param r_limits [input] Array (size: number of domains + 1) of the
* value of \e r at the boundaries of the various
* domains :
* \li \c r_limits[l] : inner boundary of the
* domain no. \c l
* \li \c r_limits[l+1] : outer boundary of the
* domain no. \c l
* The first value is not used.
* @param tab [input] equation of the surface between the nucleus and the first
* shell in the form : \f${\rm tab}(k,j) = r(\phi_k,\theta_j)\f$, where
* \f$\phi_k\f$ and \f$\theta_j\f$ are the values of the angular colocation points.
*/
Map_et(const Mg3d& mgrille, const double* r_limits,const Tbl& tab);
Map_et(const Map_et& ) ; ///< Copy constructor
Map_et(const Mg3d&, FILE* ) ; ///< Constructor from a file (see \c sauve(FILE*) )
virtual ~Map_et() ; ///< Destructor
// Assignment
// ----------
public:
/// Assignment to another \c Map_et
virtual void operator=(const Map_et& mp) ;
/// Assignment to an affine mapping.
virtual void operator=(const Map_af& mpa) ;
/// Assigns a given value to the function \f$F(\theta',\phi')\f$
void set_ff(const Valeur& ) ;
/// Assigns a given value to the function \f$G(\theta',\phi')\f$
void set_gg(const Valeur& ) ;
// Memory management
// -----------------
private:
/// Assignement of the building functions to the member \c Coords
void set_coord() ;
protected:
/// Resets all the member \c Coords
virtual void reset_coord() ;
private:
/// Construction of the polynomials \f$A(\xi)\f$ and \f$B(\xi)\f$
void fait_poly() ;
// Extraction of information
// -------------------------
public:
/** Returns the "angular" mapping for the outside of domain \c l_zone.
* Valid only for the class \c Map_af.
*/
virtual const Map_af& mp_angu(int) const ;
/** Returns a pointer on the array \c alpha (values of \f$\alpha\f$
* in each domain)
*/
const double* get_alpha() const ;
/** Returns a pointer on the array \c beta (values of \f$\beta\f$
* in each domain)
*/
const double* get_beta() const ;
/// Returns a (constant) reference to the function \f$F(\theta',\phi')\f$
const Valeur& get_ff() const ;
/// Returns a (constant) reference to the function \f$G(\theta',\phi')\f$
const Valeur& get_gg() const ;
/**
* Returns the value of the radial coordinate \e r for a given
* \f$(\xi, \theta', \phi')\f$ in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param theta [input] value of \f$\theta'\f$
* @param pphi [input] value of \f$\phi'\f$
* @return value of \f$r=R_l(\xi, \theta', \phi')\f$
*/
virtual double val_r(int l, double xi, double theta, double pphi) const ;
/**
* Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx(double rr, double theta, double pphi,
int& l, double& xi) const ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* This version enables to pass some parameters to control the
* accuracy of the computation.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param par [input/output] parameters to control the
* accuracy of the computation: \\
* \c par.get_int(0) : [input] maximum number of iterations in the
* secant method to locate \f$\xi\f$ \\
* \c par.get_int_mod(0) : [output] effective number of iterations
* used \\
* \c par.get_double(0) : [input] absolute precision in the secant
* method to locate \f$\xi\f$
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx(double rr, double theta, double pphi,
const Param& par, int& l, double& xi) const ;
/// Comparison operator (egality)
virtual bool operator==(const Map& ) const ;
/** Returns the value of the radial coordinate \e r for a given
* \f$\xi\f$ and a given collocation point in \f$(\theta', \phi')\f$
* in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param j [input] index of the collocation point in \f$\theta'\f$
* @param k [input] index of the collocation point in \f$\phi'\f$
* @return value of \f$r=R_l(\xi, {\theta'}_j, {\phi'}_k)\f$
*/
virtual double val_r_jk(int l, double xi, int j, int k) const ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point of arbitrary \e r but collocation values of \f$(\theta, \phi)\f$
* @param rr [input] value of \e r
* @param j [input] index of the collocation point in \f$\theta\f$
* @param k [input] index of the collocation point in \f$\phi\f$
* @param par [input/output] parameters to control the
* accuracy of the computation: \\
* \c par.get_int(0) : [input] maximum number of iterations in the
* secant method to locate \f$\xi\f$ \\
* \c par.get_int_mod(0) : [output] effective number of iterations
* used \\
* \c par.get_double(0) : [input] absolute precision in the secant
* method to locate \f$\xi\f$
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx_jk(double rr, int j, int k, const Param& par,
int& l, double& xi) const ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
private:
virtual ostream& operator>>(ostream &) const ; ///< Operator >>
// Modification of the radial scale
// --------------------------------
public:
/** Sets a new radial scale.
* @param lambda [input] factor by which the value of \e r is to
* be multiplied
*/
virtual void homothetie(double lambda) ;
/** Rescales the outer boundary of one domain.
* The inner boundary is unchanged. The inner boundary
* of the next domain is changed to match the new outer
* boundary.
* @param l [input] index of the domain
* @param lambda [input] factor by which the value of
* \f$R(\theta, \varphi)\f$ defining the outer boundary
* of the domain is to be multiplied.
*/
virtual void resize(int l, double lambda) ;
/** Rescales the outer boundary of the outermost domain
* in the case of non-compactified external domain.
* The inner boundary is unchanged.
* @param lambda [input] factor by which the value of the radius
* of the outermost domain is to be multiplied.
*/
void resize_extr(double lambda) ;
/// Modifies the value of \f$\alpha\f$ in domain no. \e l
void set_alpha(double alpha0, int l) ;
/// Modifies the value of \f$\beta\f$ in domain no. \e l
void set_beta(double beta0, int l) ;
// Modification of the mapping
// ---------------------------
/** Adaptation of the mapping to a given scalar field.
* Computes the functions \f$F(\theta',\phi')\f$ and \f$G(\theta',\phi')\f$
* as well as the factors \f$\alpha\f$ and \f$\beta\f$, so that the
* boundaries of some domains coincide with isosurfaces of the
* scalar field \c ent .
* @param ent [input] scalar field, the isosurfaces of which are
* used to determine the mapping
* @param par [input/output] parameters of the computation: \\
* \c par.get_int(0) : maximum number of iterations to locate
* zeros by the secant method \\
* \c par.get_int(1) : number of domains where the adjustment
* to the isosurfaces of \c ent is to be performed \\
* \c par.get_int(2) : number of domains \c nz_search where
* the isosurfaces will be searched : the routine scans the
* \c nz_search innermost domains, starting from the domain
* of index \c nz_search-1 . NB: the field \c ent must
* be continuous over these domains \\
* \c par.get_int(3) : 1 = performs the full computation,
* 0 = performs only the rescaling
* by the factor
* \c par.get_double_mod(0) \\
* \c par.get_int(4) : theta index of the collocation point
* \f$(\theta_*, \phi_*)\f$ [using the notations
* of Bonazzola, Gourgoulhon & Marck, \e Phys. \e Rev. \e D \b 58 ,
* 104020 (1998)] defining an isosurface of \c ent \\
* \c par.get_int(5) : phi index of the collocation point
* \f$(\theta_*, \phi_*)\f$ [using the notations
* of Bonazzola, Gourgoulhon & Marck, \e Phys. \e Rev. \e D \b 58 ,
* 104020 (1998)] defining an isosurface of \c ent \\
* \c par.get_int_mod(0) [output] : number of iterations
* actually used in the secant method \\
* \c par.get_double(0) : required absolute precision in the
* determination of zeros by the secant method \\
* \c par.get_double(1) : factor by which the values of \f$\lambda\f$
* and \f$\mu\f$ [using the notations
* of Bonazzola, Gourgoulhon & Marck, \e Phys. \e Rev. \e D \b 58 ,
* 104020 (1998)] will be multiplied : 1 = regular mapping,
* 0 = contracting mapping \\
* \c par.get_double(2) : factor by which all the radial distances
* will be multiplied \\
* \c par.get_tbl(0) : array of values of the field \c ent to
* define the isosurfaces.
* @param nbr\_filtre [input] Number of the last coefficients in \f$\varphi\f$ set to zero.
*/
virtual void adapt(const Cmp& ent, const Param& par, int nbr_filtre = 0) ;
// Differential operators:
// ----------------------
public:
/** Computes \f$\partial/ \partial \xi\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = \xi^2 \partial/ \partial \xi\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdxi(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = r^2 \partial/ \partial r\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdr(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$1/r \partial/ \partial \theta\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$1/u \partial/ \partial \theta = r \partial/ \partial \theta\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void srdsdt(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$1/(r\sin\theta) \partial/ \partial \phi\f$ of a \c Cmp.
* Note that in the compactified external domain (CED), it computes
* \f$1/(u\sin\theta) \partial/ \partial \phi =
* r/\sin\theta \partial/ \partial \phi\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void srstdsdp(const Cmp& ci, Cmp& resu) const ;
/** Computes \f$\partial/ \partial \xi\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdxi(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdr(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar if the description is affine and
* \f$\partial/ \partial \ln r\f$ if it is logarithmic.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdradial(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$1/r \partial/ \partial \theta\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void srdsdt(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$1/(r\sin\theta) \partial/ \partial \phi\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void srstdsdp(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$\partial/ \partial \theta\f$ of a \c Scalar.
* @param uu [input] scalar field
* @param resu [output] derivative of \c uu
*/
virtual void dsdt(const Scalar& uu, Scalar& resu) const ;
/** Computes \f$1/\sin\theta \partial/ \partial \varphi\f$ of a \c Scalar.
* @param uu [input] scalar field
* @param resu [output] derivative of \c uu
*/
virtual void stdsdp(const Scalar& uu, Scalar& resu) const ;
/** Computes the Laplacian of a scalar field.
* @param uu [input] Scalar field \e u (represented as a \c Scalar )
* the Laplacian \f$\Delta u\f$ of which is to be computed
* @param zec_mult_r [input] Determines the quantity computed in
* the compactified external domain (CED) : \\
* zec_mult_r = 0 : \f$\Delta u\f$ \\
* zec_mult_r = 2 : \f$r^2 \, \Delta u\f$ \\
* zec_mult_r = 4 (default) : \f$r^4 \, \Delta u\f$
* @param lap [output] Laplacian of \e u
*/
virtual void laplacien(const Scalar& uu, int zec_mult_r,
Scalar& lap) const ;
/// Computes the Laplacian of a scalar field (\c Cmp version).
virtual void laplacien(const Cmp& uu, int zec_mult_r,
Cmp& lap) const ;
/** Computes the angular Laplacian of a scalar field.
* @param uu [input] Scalar field \e u (represented as a \c Scalar)
* the Laplacian \f$\Delta u\f$ of which is to be computed
* @param lap [output] Angular Laplacian of \e u (see documentation
* of \c Scalar
*/
virtual void lapang(const Scalar& uu, Scalar& lap) const ;
/** Computes the radial primitive which vanishes for \f$r\to \infty\f$.
* i.e. the function
* \f$ F(r,\theta,\varphi) = \int_r^\infty f(r',\theta,\varphi) \, dr' \f$
*
* @param uu [input] function \e f (must have a \c dzpuis = 2)
* @param resu [input] function \e F
* @param null_infty if true (default), the primitive is null
* at infinity (or on the grid boundary). \e F is null at the
* center otherwise
*/
virtual void primr(const Scalar& uu, Scalar& resu,
bool null_infty) const ;
/** Computes the integral over all space of a \c Cmp.
* The computed quantity is
* \f$\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi\f$.
* The routine allocates a \c Tbl (size: \c mg->nzone ) to store
* the result (partial integral) in each domain and returns a pointer
* to it.
*/
virtual Tbl* integrale(const Cmp&) const ;
// PDE resolution :
// --------------
public:
/** Computes the solution of a scalar Poisson equation.
*
* Following the method explained in Sect. III.C of Bonazzola,
* Gourgoulhon & Marck, \e Phys. \e Rev. \e D \b 58 , 104020 (1998),
* the Poisson equation \f$\Delta u = \sigma\f$ is re-written
* as \f$a \tilde\Delta u = \sigma + R(u)\f$, where \f$\tilde\Delta\f$
* is the Laplacian in an affine mapping and \e R(u) contains the
* terms generated by the deviation of the mapping \c *this
* from spherical symmetry. This equation is solved by iterations.
* At each step \e J the equation effectively solved is
* \f$\tilde\Delta u^{J+1} = s^J\f$ where
* \f[
* s^J = 1/a_l^{\rm max} \{ {\tt source} + R(u^J) + (a_l^{\rm max}-a)
* [ \lambda s^{J-1} + (1-\lambda) s^{J-2} ] \} \ ,
* \f]
* with \f$a_l^{\rm max} := \max(a)\f$ in domain no. \e l and \f$\lambda\f$
* is a relaxation parameter.
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* @param par [input/output] parameters for the iterative method: \\
* \c par.get_int(0) : [input] maximum number of iterations \\
* \c par.get_double(0) : [input] relaxation parameter \f$\lambda\f$ \\
* \c par.get_double(1) : [input] required precision: the iterative
* method is stopped as soon as the relative difference between
* \f$u^J\f$ and \f$u^{J-1}\f$ is greater than \c par.get_double(1) \\
* \c par.get_cmp_mod(0) : [input/output] input : \c Cmp
* containing \f$s^{J-1}\f$ (cf. the above equation) to
* start the iteration (if nothing is known a priori,
* this \c Cmp must be set to zero); output: value
* of \f$s^{J-1}\f$, to used in a next call to the routine \\
* \c par.get_int_mod(0) : [output] number of iterations
* actually used to get the solution.
*
* @param uu [input/output] input : previously computed value of \e u
* to start the iteration (term \e R(u) ) (if nothing is known a
* priori, \c uu must be set to zero); output: solution \e u
* with the boundary condition \e u =0 at spatial infinity.
*/
virtual void poisson(const Cmp& source, Param& par, Cmp& uu) const ;
/** Computes the solution of a scalar Poisson equation with a Tau method.
*
* Following the method explained in Sect. III.C of Bonazzola,
* Gourgoulhon & Marck, \e Phys. \e Rev. \e D \b 58 , 104020 (1998),
* the Poisson equation \f$\Delta u = \sigma\f$ is re-written
* as \f$a \tilde\Delta u = \sigma + R(u)\f$, where \f$\tilde\Delta\f$
* is the Laplacian in an affine mapping and \e R(u) contains the
* terms generated by the deviation of the mapping \c *this
* from spherical symmetry. This equation is solved by iterations.
* At each step \e J the equation effectively solved is
* \f$\tilde\Delta u^{J+1} = s^J\f$ where
* \f[
* s^J = 1/a_l^{\rm max} \{ {\tt source} + R(u^J) + (a_l^{\rm max}-a)
* [ \lambda s^{J-1} + (1-\lambda) s^{J-2} ] \} \ ,
* \f]
* with \f$a_l^{\rm max} := \max(a)\f$ in domain no. \e l and \f$\lambda\f$
* is a relaxation parameter.
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* @param par [input/output] parameters for the iterative method: \\
* \c par.get_int(0) : [input] maximum number of iterations \\
* \c par.get_double(0) : [input] relaxation parameter \f$\lambda\f$ \\
* \c par.get_double(1) : [input] required precision: the iterative
* method is stopped as soon as the relative difference between
* \f$u^J\f$ and \f$u^{J-1}\f$ is greater than \c par.get_double(1) \\
* \c par.get_cmp_mod(0) : [input/output] input : \c Cmp
* containing \f$s^{J-1}\f$ (cf. the above equation) to
* start the iteration (if nothing is known a priori,
* this \c Cmp must be set to zero); output: value
* of \f$s^{J-1}\f$, to used in a next call to the routine \\
* \c par.get_int_mod(0) : [output] number of iterations
* actually used to get the solution.
*
* @param uu [input/output] input : previously computed value of \e u
* to start the iteration (term \e R(u) ) (if nothing is known a
* priori, \c uu must be set to zero); output: solution \e u
* with the boundary condition \e u =0 at spatial infinity.
*/
virtual void poisson_tau(const Cmp& source, Param& par, Cmp& uu) const ;
virtual void poisson_falloff(const Cmp& source, Param& par, Cmp& uu,
int k_falloff) const ;
virtual void poisson_ylm(const Cmp& source, Param& par, Cmp& uu,
int nylm, double* intvec) const ;
/** Computes the solution of a scalar Poisson equation.
* The regularized source
* @param source [input] source \f$\sigma\f$ of the Poisson equation
* \f$\Delta u = \sigma\f$.
* @param k_div [input] regularization degree of the procedure
* @param nzet [input] number of domains covering the star
* @param unsgam1 [input] parameter \f$1/(\gamma-1)\f$ where \f$\gamma\f$
* denotes the adiabatic index.
* @param par [input/output] parameters for the iterative method: \\
* \c par.get_int(0) : [input] maximum number of iterations \\
* \c par.get_double(0) : [input] relaxation parameter
* \f$\lambda\f$ \\
* \c par.get_double(1) : [input] required precision: the
* iterative method is stopped as soon as the relative
* difference between \f$u^J\f$ and \f$u^{J-1}\f$ is greater than
* \c par.get_double(1) \\
* \c par.get_cmp_mod(0) : [input/output] input : \c Cmp
* containing \f$s^{J-1}\f$ (cf. the above equation) to
* start the iteration (if nothing is known a priori,
* this \c Cmp must be set to zero); output: value
* of \f$s^{J-1}\f$, to used in a next call to the routine \\
* \c par.get_int_mod(0) : [output] number of iterations
* actually used to get the solution.
* @param uu [input/output] input : previously computed value of \e u
* to start the iteration (term \e R(u) ) (if nothing is known a
* priori, \c uu must be set to zero); output: solution \e u
* with the boundary condition \e u =0 at spatial infinity.
* @param uu_regu [output] solution of the regular part of
* the source.
* @param uu_div [output] solution of the diverging part of
* the source.
* @param duu_div [output] derivative of the diverging potential
* @param source_regu [output] regularized source
* @param source_div [output] diverging part of the source
*/
virtual void poisson_regular(const Cmp& source, int k_div, int nzet,
double unsgam1, Param& par, Cmp& uu,
Cmp& uu_regu, Cmp& uu_div,
Tenseur& duu_div, Cmp& source_regu,
Cmp& source_div) const ;
/** Computes the solution of the generalized angular Poisson equation.
* The generalized angular Poisson equation is
* \f$\Delta_{\theta\varphi} u + \lambda u = \sigma\f$,
* where \f$\Delta_{\theta\varphi} u := \frac{\partial^2 u}
* {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial u}
* {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 u}
* {\partial \varphi^2}\f$.
*
* @param source [input] source \f$\sigma\f$ of the equation
* \f$\Delta_{\theta\varphi} u + \lambda u = \sigma\f$.
* @param par [input/output] possible parameters to control the
* resolution of the Poisson equation. See the actual implementation
* in the derived class of \c Map for documentation.
* @param uu [input/output] solution \e u
* @param lambda [input] coefficient \f$\lambda\f$ in the above equation
* (default value = 0)
*/
virtual void poisson_angu(const Scalar& source, Param& par,
Scalar& uu, double lambda=0) const ;
/**
* Internal function intended to be used by \c Map::poisson_vect
* and \c Map::poisson_vect_oohara . It constructs the sets of
* parameters used for each scalar Poisson equation from the one for
* the vectorial one.
*
* @param para [input] : the \c Param used for the resolution of
* the vectorial Poisson equation : \\
* \c para.int() maximum number of iteration.\\
* \c para.double(0) relaxation parameter.\\
* \c para.double(1) required precision. \\
* \c para.tenseur_mod() source of the vectorial part at the previous
* step.\\
* \c para.cmp_mod() source of the scalar part at the previous
* step.
*
* @param i [input] number of the scalar Poisson equation that is being
* solved (values from 0 to 2 for the componants of the vectorial part
* and 3 for the scalar one).
*
* @return the pointer on the parameter set used for solving the scalar
* Poisson equation labelled by \e i .
*/
virtual Param* donne_para_poisson_vect (Param& para, int i) const ;
/**
* Not yet implemented.
*/
virtual void poisson_frontiere (const Cmp&, const Valeur&, int, int,
Cmp&, double = 0., double = 0.) const ;
virtual void poisson_frontiere_double (const Cmp& source,
const Valeur& lim_func, const Valeur& lim_der,
int num_zone, Cmp& pot) const ;
/**
* Computes the solution of a Poisson equation in the shell .
* imposing a boundary condition at the surface of the star
*
* @param source [input] : source of the equation.
* @param limite [input] : \c limite[num_front] contains the angular
* function being the boudary condition.
* @param par [input] : parameters of the computation.
* @param pot [output] : result.
*/
virtual void poisson_interne (const Cmp& source, const Valeur& limite,
Param& par, Cmp& pot) const ;
/** Computes the solution of a 2-D Poisson equation.
* The 2-D Poisson equation writes
* \f[
* {\partial^2 u\over\partial r^2} +
* {1\over r} {\partial u \over \partial r} +
* {1\over r^2} {\partial^2 u\over\partial \theta^2} =
* \sigma \ .
* \f]
*
* @param source_mat [input] Compactly supported part of
* the source \f$\sigma\f$ of the 2-D Poisson equation (typically
* matter terms)
* @param source_quad [input] Non-compactly supported part of
* the source \f$\sigma\f$ of the 2-D Poisson equation (typically
* quadratic terms)
* @param par [input/output] Parameters to control the resolution : \\
* \c par.get_double_mod(0) : [output] constant \c lambda
* such that the source of the equation effectively solved
* is \c source_mat + lambda * source_quad , in order to
* fulfill the virial identity GRV2. \\
* If the theta basis is \c T_SIN_I , the following arguments
* are required: \\
* \c par.get_int(0) : [input] maximum number of iterations \\
* \c par.get_double(0) : [input] relaxation parameter \\
* \c par.get_double(1) : [input] required precision: the iterative
* method is stopped as soon as the relative difference between
* \f$u^J\f$ and \f$u^{J-1}\f$ is greater than \c par.get_double(1) \\
* \c par.get_cmp_mod(0) : [input/output] input : \c Cmp
* containing \f$s^{J-1}\f$ to
* start the iteration (if nothing is known a priori,
* this \c Cmp must be set to zero); output: value
* of \f$s^{J-1}\f$, to used in a next call to the routine \\
* \c par.get_int_mod(0) : [output] number of iterations
* actually used to get the solution.
*
* @param uu [input/output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
virtual void poisson2d(const Cmp& source_mat, const Cmp& source_quad,
Param& par, Cmp& uu) const ;
/**
* Not yet implemented.
*/
virtual void dalembert(Param& par, Scalar& fJp1, const Scalar& fJ,
const Scalar& fJm1, const Scalar& source) const ;
// Building functions for the Coord's
// ----------------------------------
friend Mtbl* map_et_fait_r(const Map* ) ;
friend Mtbl* map_et_fait_tet(const Map* ) ;
friend Mtbl* map_et_fait_phi(const Map* ) ;
friend Mtbl* map_et_fait_sint(const Map* ) ;
friend Mtbl* map_et_fait_cost(const Map* ) ;
friend Mtbl* map_et_fait_sinp(const Map* ) ;
friend Mtbl* map_et_fait_cosp(const Map* ) ;
friend Mtbl* map_et_fait_x(const Map* ) ;
friend Mtbl* map_et_fait_y(const Map* ) ;
friend Mtbl* map_et_fait_z(const Map* ) ;
friend Mtbl* map_et_fait_xa(const Map* ) ;
friend Mtbl* map_et_fait_ya(const Map* ) ;
friend Mtbl* map_et_fait_za(const Map* ) ;
friend Mtbl* map_et_fait_xsr(const Map* ) ;
friend Mtbl* map_et_fait_dxdr(const Map* ) ;
friend Mtbl* map_et_fait_drdt(const Map* ) ;
friend Mtbl* map_et_fait_stdrdp(const Map* ) ;
friend Mtbl* map_et_fait_srdrdt(const Map* ) ;
friend Mtbl* map_et_fait_srstdrdp(const Map* ) ;
friend Mtbl* map_et_fait_sr2drdt(const Map* ) ;
friend Mtbl* map_et_fait_sr2stdrdp(const Map* ) ;
friend Mtbl* map_et_fait_d2rdx2(const Map* ) ;
friend Mtbl* map_et_fait_lapr_tp(const Map* ) ;
friend Mtbl* map_et_fait_d2rdtdx(const Map* ) ;
friend Mtbl* map_et_fait_sstd2rdpdx(const Map* ) ;
friend Mtbl* map_et_fait_sr2d2rdt2(const Map* ) ;
friend Mtbl* map_et_fait_rsxdxdr(const Map* ) ;
friend Mtbl* map_et_fait_rsx2drdx(const Map* ) ;
};
Mtbl* map_et_fait_r(const Map* ) ;
Mtbl* map_et_fait_tet(const Map* ) ;
Mtbl* map_et_fait_phi(const Map* ) ;
Mtbl* map_et_fait_sint(const Map* ) ;
Mtbl* map_et_fait_cost(const Map* ) ;
Mtbl* map_et_fait_sinp(const Map* ) ;
Mtbl* map_et_fait_cosp(const Map* ) ;
Mtbl* map_et_fait_x(const Map* ) ;
Mtbl* map_et_fait_y(const Map* ) ;
Mtbl* map_et_fait_z(const Map* ) ;
Mtbl* map_et_fait_xa(const Map* ) ;
Mtbl* map_et_fait_ya(const Map* ) ;
Mtbl* map_et_fait_za(const Map* ) ;
Mtbl* map_et_fait_xsr(const Map* ) ;
Mtbl* map_et_fait_dxdr(const Map* ) ;
Mtbl* map_et_fait_drdt(const Map* ) ;
Mtbl* map_et_fait_stdrdp(const Map* ) ;
Mtbl* map_et_fait_srdrdt(const Map* ) ;
Mtbl* map_et_fait_srstdrdp(const Map* ) ;
Mtbl* map_et_fait_sr2drdt(const Map* ) ;
Mtbl* map_et_fait_sr2stdrdp(const Map* ) ;
Mtbl* map_et_fait_d2rdx2(const Map* ) ;
Mtbl* map_et_fait_lapr_tp(const Map* ) ;
Mtbl* map_et_fait_d2rdtdx(const Map* ) ;
Mtbl* map_et_fait_sstd2rdpdx(const Map* ) ;
Mtbl* map_et_fait_sr2d2rdt2(const Map* ) ;
Mtbl* map_et_fait_rsxdxdr(const Map* ) ;
Mtbl* map_et_fait_rsx2drdx(const Map* ) ;
//------------------------------------//
// class Map_log //
//------------------------------------//
#define AFFINE 0
#define LOG 1
/**
* Logarithmic radial mapping. \ingroup (map)
*
* This mapping is a variation of the affine one.
*
* In each domain the description can be either affine (cf. Map_af documentation) or
* logarithmic. In that case (implemented only in the shells) we have
*
* \li \f$\ln r=\alpha \xi + \beta\f$,
* where \f$\alpha\f$ and \f$\beta\f$ are constant in each domain.
*
*
*/
class Map_log : public Map_radial {
// Data :
// ----
private:
/// Array (size: \c mg->nzone ) of the values of \f$\alpha\f$ in each domain
Tbl alpha ;
/// Array (size: \c mg->nzone ) of the values of \f$\beta\f$ in each domain
Tbl beta ;
/** Array (size: \c mg->nzone ) of the type of variable in each domain.
* The possibles types are AFFINE and LOG.
**/
Itbl type_var ;
public:
/**
* Same as dxdr if the domains where the description is affine and
* \f$ \partial x / \partial \ln r\f$ where it is logarithmic.
*/
Coord dxdlnr ;
private:
void set_coord() ;
// Constructors, destructor :
// ------------------------
public:
/**
* Standard Constructor
* @param mgrille [input] Multi-domain grid on which the mapping is defined
* @param r_limits [input] Tbl (size: number of domains + 1) of the
* value of \e r at the boundaries of the various
* domains :
* \li \c r_limits[l] : inner boundary of the
* domain no. \c l
* \li \c r_limits[l+1] : outer boundary of the
* domain no. \c l
* @param type_var [input] Array (size: number of domains) defining the type f mapping in each domain.
*/
Map_log (const Mg3d& mgrille, const Tbl& r_limits, const Itbl& typevar) ;
Map_log (const Map_log& ) ; ///< Copy constructor
Map_log (const Mg3d&, FILE* ) ; ///< Constructor from a file (see \c sauve(FILE*)
virtual ~Map_log() ; ///< Destructor
/** Returns the "angular" mapping for the outside of domain \c l_zone.
* Valid only for the class \c Map_af.
*/
virtual const Map_af& mp_angu(int) const ;
/// Returns \f$\alpha\f$ in the domain \c l
double get_alpha (int l) const {return alpha(l) ;} ;
/// Returns \f$\beta\f$ in the domain \c l
double get_beta (int l) const {return beta(l) ;} ;
/// Returns the type of description in the domain \c l
int get_type (int l) const {return type_var(l) ;} ;
/**
* General elliptic solver. The field is zero at infinity.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
**/
void sol_elliptic (Param_elliptic& params,
const Scalar& so, Scalar& uu) const ;
/**
* General elliptic solver including inner boundary conditions.
* The field is zero at infinity.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
* @param bound [input] : the boundary condition
* @param fact_dir : 1 Dirchlet condition, 0 Neumann condition
* @param fact_neu : 0 Dirchlet condition, 1 Neumann condition
**/
void sol_elliptic_boundary (Param_elliptic& params,
const Scalar& so, Scalar& uu, const Mtbl_cf& bound,
double fact_dir, double fact_neu ) const ;
/** General elliptic solver including inner boundary conditions, the bound being
* given as a Scalar on a mono-domain angular grid.
**/
void sol_elliptic_boundary (Param_elliptic& params,
const Scalar& so, Scalar& uu, const Scalar& bound,
double fact_dir, double fact_neu ) const ;
/**
* General elliptic solver.
* The equation is not solved in the compactified domain.
*
* @param params [input] : the operators and variables to be uses.
* @param so [input] : the source.
* @param uu [output] : the solution.
* @param val [input] : value at the last shell.
**/
void sol_elliptic_no_zec (Param_elliptic& params,
const Scalar& so, Scalar& uu, double) const ;
virtual void sauve(FILE*) const ; ///< Save in a file
/// Assignment to an affine mapping.
virtual void operator=(const Map_af& mpa) ;
virtual ostream& operator>> (ostream&) const ; ///< Operator >>
/**
* Returns the value of the radial coordinate \e r for a given
* \f$(\xi, \theta', \phi')\f$ in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param theta [input] value of \f$\theta'\f$
* @param pphi [input] value of \f$\phi'\f$
* @return value of \f$r=R_l(\xi, \theta', \phi')\f$
*/
virtual double val_r (int l, double xi, double theta, double pphi) const ;
/**
* Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx (double rr, double theta, double pphi, int& l, double& xi) const ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point given by its physical coordinates \f$(r, \theta, \phi)\f$.
* @param rr [input] value of \e r
* @param theta [input] value of \f$\theta\f$
* @param pphi [input] value of \f$\phi\f$
* @param par [] unused by the \c Map_af version
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx (double rr, double theta, double pphi, const Param& par, int& l, double& xi) const ;
virtual bool operator== (const Map&) const ; /// < Comparison operator
/** Returns the value of the radial coordinate \e r for a given
* \f$\xi\f$ and a given collocation point in \f$(\theta', \phi')\f$
* in a given domain.
* @param l [input] index of the domain
* @param xi [input] value of \f$\xi\f$
* @param j [input] index of the collocation point in \f$\theta'\f$
* @param k [input] index of the collocation point in \f$\phi'\f$
* @return value of \f$r=R_l(\xi, {\theta'}_j, {\phi'}_k)\f$
*/
virtual double val_r_jk (int l, double xi, int j, int k) const ;
/** Computes the domain index \e l and the value of \f$\xi\f$ corresponding
* to a point of arbitrary \e r but collocation values of \f$(\theta, \phi)\f$
* @param rr [input] value of \e r
* @param j [input] index of the collocation point in \f$\theta\f$
* @param k [input] index of the collocation point in \f$\phi\f$
* @param par [] unused by the \c Map_af version
* @param l [output] value of the domain index
* @param xi [output] value of \f$\xi\f$
*/
virtual void val_lx_jk (double rr, int j, int k, const Param& par, int& l, double& xi) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = r^2 \partial/ \partial r\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdr (const Scalar& ci, Scalar& resu) const ;
/** Computes \f$\partial/ \partial \xi\f$ of a \c Scalar.
* Note that in the compactified external domain (CED), it computes
* \f$-\partial/ \partial u = \xi^2 \partial/ \partial \xi\f$.
* @param ci [input] field to consider
* @param resu [output] derivative of \c ci
*/
virtual void dsdxi (const Scalar& ci, Scalar& resu) const ;
/** Computes \f$\partial/ \partial r\f$ of a \c Scalar if the description is affine and
* \f$\partial/ \partial \ln r\f$ if it is logarithmic.
* Note that in the compactified external domain (CED), the \c dzpuis
* flag of the output is 2 if the input has \c dzpuis = 0, and
* is increased by 1 in other cases.
* @param uu [input] field to consider
* @param resu [output] derivative of \c uu
*/
virtual void dsdradial (const Scalar& uu, Scalar& resu) const ;
virtual void homothetie (double) ; /// < Not implemented
virtual void resize (int, double) ;/// < Not implemented
virtual void adapt (const Cmp&, const Param&, int) ;/// < Not implemented
virtual void dsdr (const Cmp&, Cmp&) const ;/// < Not implemented
virtual void dsdxi (const Cmp&, Cmp&) const ;/// < Not implemented
virtual void srdsdt (const Cmp&, Cmp&) const ;/// < Not implemented
virtual void srstdsdp (const Cmp&, Cmp&) const ;/// < Not implemented
virtual void srdsdt (const Scalar&, Scalar&) const ;/// < Not implemented
virtual void srstdsdp (const Scalar&, Scalar&) const ;/// < Not implemented
virtual void dsdt (const Scalar&, Scalar&) const ;/// < Not implemented
virtual void stdsdp (const Scalar&, Scalar&) const ;/// < Not implemented
virtual void laplacien (const Scalar&, int, Scalar&) const ;/// < Not implemented
virtual void laplacien (const Cmp&, int, Cmp&) const ;/// < Not implemented
virtual void lapang (const Scalar&, Scalar&) const ;/// < Not implemented
virtual void primr(const Scalar&, Scalar&, bool) const ;/// < Not implemented
virtual Tbl* integrale (const Cmp&) const ;/// < Not implemented
virtual void poisson (const Cmp&, Param&, Cmp&) const ;/// < Not implemented
virtual void poisson_tau (const Cmp&, Param&, Cmp&) const ;/// < Not implemented
virtual void poisson_falloff(const Cmp&, Param&, Cmp&, int) const ;/// < Not implemented
virtual void poisson_ylm(const Cmp&, Param&, Cmp&, int, double*) const ;/// < Not implemented
virtual void poisson_regular (const Cmp&, int, int, double, Param&, Cmp&, Cmp&, Cmp&,
Tenseur&, Cmp&, Cmp&) const ;/// < Not implemented
virtual void poisson_angu (const Scalar&, Param&, Scalar&, double=0) const ;/// < Not implemented
virtual Param* donne_para_poisson_vect (Param&, int) const ;/// < Not implemented
virtual void poisson_frontiere (const Cmp&, const Valeur&, int, int, Cmp&, double = 0., double = 0.) const ;/// < Not implemented
virtual void poisson_frontiere_double (const Cmp&, const Valeur&, const Valeur&, int, Cmp&) const ;/// < Not implemented
virtual void poisson_interne (const Cmp&, const Valeur&, Param&, Cmp&) const ;/// < Not implemented
virtual void poisson2d (const Cmp&, const Cmp&, Param&, Cmp&) const ;/// < Not implemented
virtual void dalembert (Param&, Scalar&, const Scalar&, const Scalar&, const Scalar&) const ;/// < Not implemented
// Building functions for the Coord's
// ----------------------------------
friend Mtbl* map_log_fait_r(const Map* ) ;
friend Mtbl* map_log_fait_tet(const Map* ) ;
friend Mtbl* map_log_fait_phi(const Map* ) ;
friend Mtbl* map_log_fait_sint(const Map* ) ;
friend Mtbl* map_log_fait_cost(const Map* ) ;
friend Mtbl* map_log_fait_sinp(const Map* ) ;
friend Mtbl* map_log_fait_cosp(const Map* ) ;
friend Mtbl* map_log_fait_x(const Map* ) ;
friend Mtbl* map_log_fait_y(const Map* ) ;
friend Mtbl* map_log_fait_z(const Map* ) ;
friend Mtbl* map_log_fait_xa(const Map* ) ;
friend Mtbl* map_log_fait_ya(const Map* ) ;
friend Mtbl* map_log_fait_za(const Map* ) ;
friend Mtbl* map_log_fait_xsr(const Map* ) ;
friend Mtbl* map_log_fait_dxdr(const Map* ) ;
friend Mtbl* map_log_fait_drdt(const Map* ) ;
friend Mtbl* map_log_fait_stdrdp(const Map* ) ;
friend Mtbl* map_log_fait_srdrdt(const Map* ) ;
friend Mtbl* map_log_fait_srstdrdp(const Map* ) ;
friend Mtbl* map_log_fait_sr2drdt(const Map* ) ;
friend Mtbl* map_log_fait_sr2stdrdp(const Map* ) ;
friend Mtbl* map_log_fait_d2rdx2(const Map* ) ;
friend Mtbl* map_log_fait_lapr_tp(const Map* ) ;
friend Mtbl* map_log_fait_d2rdtdx(const Map* ) ;
friend Mtbl* map_log_fait_sstd2rdpdx(const Map* ) ;
friend Mtbl* map_log_fait_sr2d2rdt2(const Map* ) ;
friend Mtbl* map_log_fait_dxdlnr(const Map* ) ;
};
Mtbl* map_log_fait_r(const Map* ) ;
Mtbl* map_log_fait_tet(const Map* ) ;
Mtbl* map_log_fait_phi(const Map* ) ;
Mtbl* map_log_fait_sint(const Map* ) ;
Mtbl* map_log_fait_cost(const Map* ) ;
Mtbl* map_log_fait_sinp(const Map* ) ;
Mtbl* map_log_fait_cosp(const Map* ) ;
Mtbl* map_log_fait_x(const Map* ) ;
Mtbl* map_log_fait_y(const Map* ) ;
Mtbl* map_log_fait_z(const Map* ) ;
Mtbl* map_log_fait_xa(const Map* ) ;
Mtbl* map_log_fait_ya(const Map* ) ;
Mtbl* map_log_fait_za(const Map* ) ;
Mtbl* map_log_fait_xsr(const Map* ) ;
Mtbl* map_log_fait_dxdr(const Map* ) ;
Mtbl* map_log_fait_drdt(const Map* ) ;
Mtbl* map_log_fait_stdrdp(const Map* ) ;
Mtbl* map_log_fait_srdrdt(const Map* ) ;
Mtbl* map_log_fait_srstdrdp(const Map* ) ;
Mtbl* map_log_fait_sr2drdt(const Map* ) ;
Mtbl* map_log_fait_sr2stdrdp(const Map* ) ;
Mtbl* map_log_fait_d2rdx2(const Map* ) ;
Mtbl* map_log_fait_lapr_tp(const Map* ) ;
Mtbl* map_log_fait_d2rdtdx(const Map* ) ;
Mtbl* map_log_fait_sstd2rdpdx(const Map* ) ;
Mtbl* map_log_fait_sr2d2rdt2(const Map* ) ;
Mtbl* map_log_fait_dxdlnr (const Map*) ;
}
#endif
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