LORENE
tslice_check_einstein.C
1 /*
2  * Methods of class Time_slice to check Einstein equation solutions.
3  *
4  * (see file time_slice.h for documentation).
5  *
6  */
7 
8 /*
9  * Copyright (c) 2004 Eric Gourgoulhon, Jose Luis Jaramillo & Jerome Novak
10  *
11  * This file is part of LORENE.
12  *
13  * LORENE is free software; you can redistribute it and/or modify
14  * it under the terms of the GNU General Public License version 2
15  * as published by the Free Software Foundation.
16  *
17  * LORENE is distributed in the hope that it will be useful,
18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20  * GNU General Public License for more details.
21  *
22  * You should have received a copy of the GNU General Public License
23  * along with LORENE; if not, write to the Free Software
24  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25  *
26  */
27 
28 
29 
30 /*
31  * $Id: tslice_check_einstein.C,v 1.11 2016/12/05 16:18:19 j_novak Exp $
32  * $Log: tslice_check_einstein.C,v $
33  * Revision 1.11 2016/12/05 16:18:19 j_novak
34  * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
35  *
36  * Revision 1.10 2014/10/13 08:53:47 j_novak
37  * Lorene classes and functions now belong to the namespace Lorene.
38  *
39  * Revision 1.9 2014/10/06 15:13:22 j_novak
40  * Modified #include directives to use c++ syntax.
41  *
42  * Revision 1.8 2010/10/20 07:58:09 j_novak
43  * Better implementation of the explicit time-integration. Not fully-tested yet.
44  *
45  * Revision 1.7 2007/11/06 12:10:56 j_novak
46  * Corrected some mistakes.
47  *
48  * Revision 1.6 2007/11/06 11:53:34 j_novak
49  * Use of contravariant version of the 3+1 equations.
50  *
51  * Revision 1.5 2007/06/28 14:40:36 j_novak
52  * Dynamical check: the fields in the last domain are set to zero to avoid dzpuis problems
53  *
54  * Revision 1.4 2004/05/12 15:24:20 e_gourgoulhon
55  * Reorganized the #include 's, taking into account that
56  * time_slice.h contains now an #include "metric.h".
57  *
58  * Revision 1.3 2004/04/07 07:58:21 e_gourgoulhon
59  * Constructor as Minkowski slice: added call to std_spectral_base()
60  * after setting the lapse to 1.
61  *
62  * Revision 1.2 2004/04/05 12:38:45 j_novak
63  * Minor modifs to prevent some warnings.
64  *
65  * Revision 1.1 2004/04/05 11:54:20 j_novak
66  * First operational (but not tested!) version of checks of Eintein equations.
67  *
68  *
69  * $Header: /cvsroot/Lorene/C++/Source/Time_slice/tslice_check_einstein.C,v 1.11 2016/12/05 16:18:19 j_novak Exp $
70  *
71  */
72 
73 // C headers
74 #include <cstdlib>
75 #include <cassert>
76 
77 // Lorene headers
78 #include "time_slice.h"
79 #include "unites.h"
80 
81 namespace Lorene {
83  ostream& ost, bool verb) const {
84  using namespace Unites ;
85 
86  bool vacuum = ( energy_density == 0x0 ) ;
87 
88  Scalar field = trk() * trk() - contract( k_uu(), 0, 1, k_dd(), 0, 1 ) ;
89 
90  field.dec_dzpuis() ; // dzpuis: 4 -> 3
91 
92  field += gam().ricci_scal() ;
93 
94  const Scalar* matter ;
95  if (vacuum)
96  matter = new Scalar (0*field) ;
97  else
98  matter = energy_density ;
99 
100  if (verb) ost << endl ;
101  const char* comment = 0x0 ;
102  if (verb) comment = "Check of the Hamiltonian constraint" ;
103  Tbl resu = maxabs(field - (4*qpig) * (*matter), comment, ost,verb ) ;
104  if (verb) ost << endl ;
105 
106  if (vacuum) delete matter ;
107 
108  return resu ;
109 
110 }
111 
113  ostream& ost, bool verb) const {
114  using namespace Unites ;
115 
116  bool vacuum = ( momentum_density == 0x0 ) ;
117 
118  Vector field = k_uu().divergence(gam()) - trk().derive_con(gam()) ;
119 
120 
121  const Vector* matter ;
122  if (vacuum)
123  matter = new Vector (0*field) ;
124  else {
125  assert (momentum_density->get_index_type(0) == CON) ;
126  matter = momentum_density ;
127  }
128 
129  if (verb) ost << endl ;
130  const char* comment = 0x0 ;
131  if (verb) comment = "Check of the momentum constraint" ;
132  Tbl resu = maxabs(field - (2*qpig) * (*matter), comment, ost, verb ) ;
133 
134  if (verb) ost << endl ;
135 
136  if (vacuum) delete matter ;
137 
138  return resu ;
139 
140 }
141 
143  const Scalar* energy_density,
144  ostream& ost, bool verb) const {
145 
146  using namespace Unites ;
147 
148  bool vacuum = ( ( strain_tensor == 0x0 ) && ( energy_density == 0x0 ) ) ;
149 
150  Sym_tensor dyn_lhs = (k_dd_evol.time_derive(jtime, scheme_order)).up_down(gam()) ;
151  int nz = dyn_lhs.get_mp().get_mg()->get_nzone() ;
152  dyn_lhs.annule_domain(nz-1) ;
153  dyn_lhs = dyn_lhs - k_dd().derive_lie(beta()).up_down(gam()) ;
154  dyn_lhs.annule_domain(nz-1) ;
155 
156  const Sym_tensor* matter ;
157  if (vacuum)
158  matter = new Sym_tensor(0 * dyn_lhs) ;
159  else {
160  const Scalar* ener = 0x0 ;
161  const Sym_tensor* sij = 0x0 ;
162  bool new_e = false ;
163  bool new_s = false ;
164  if (energy_density == 0x0) {
165  ener = new Scalar ( 0 * nn() ) ;
166  new_e = true ;
167  }
168  else {
169  ener = energy_density ;
170  if (strain_tensor == 0x0) {
171  sij = new Sym_tensor(0 * dyn_lhs) ;
172  new_s = true ;
173  }
174  else
175  sij = strain_tensor ;
176  }
177  matter = new Sym_tensor( (sij->trace(gam()) - *ener)*gam().con()
178  - 2*(*sij) ) ;
179  if (new_e) delete ener ;
180  if (new_s) delete sij ;
181  }
182 
183  Sym_tensor dyn_rhs = nn()*( (gam().ricci().up_down(gam()) + trk()*k_uu()
184  + qpig * (*matter))) ;
185  dyn_rhs.annule_domain(nz-1) ;
186  dyn_rhs = dyn_rhs - 2*nn()*contract(k_uu(), 1, k_dd().up(0, gam()), 1) ;
187  dyn_rhs.annule_domain(nz-1) ;
188  dyn_rhs = dyn_rhs - nn().derive_con(gam()).derive_con(gam()) ;
189  dyn_rhs.annule_domain(nz-1) ;
190 
191  if (verb) ost << endl ;
192  const char* comment = 0x0 ;
193  if (verb) comment = "Check of the dynamical equations" ;
194  Tbl resu_tmp = maxabs(dyn_lhs - dyn_rhs, comment, ost, verb) ;
195 
196  if (verb) ost << endl ;
197 
198  if (vacuum) delete matter ;
199 
200  Tbl resu(4, 4, resu_tmp.get_dim(0)) ;
201  resu.annule_hard() ; //## To initialize resu(0,0,...) which
202  // does not correspond to a valid component
203 
204  for (int i=1; i<=3; i++) {
205  for (int j=1; j<=i; j++) {
206  Itbl idx(2) ;
207  idx.set(0) = i ;
208  idx.set(1) = j ;
209  int pos = dyn_lhs.position(idx) ;
210  assert (dyn_rhs.position(idx) == pos) ;
211 
212  for (int lz=0; lz<resu_tmp.get_dim(0); lz++)
213  resu.set(i,j,lz) = resu_tmp(pos, lz) ;
214  }
215  }
216 
217  return resu ;
218 
219 }
220 }
virtual const Vector & beta() const
shift vector at the current time step (jtime )
void annule_domain(int l)
Sets the Tensor to zero in a given domain.
Definition: tensor.C:675
Tbl maxabs(const Tensor &aa, const char *comment=0x0, ostream &ost=cout, bool verb=true)
Maxima in each domain of the absolute values of the tensor components.
virtual const Sym_tensor & con() const
Read-only access to the contravariant representation.
Definition: metric.C:293
int & set(int i)
Read/write of a particular element (index i ) (1D case)
Definition: itbl.h:247
Lorene prototypes.
Definition: app_hor.h:67
Standard units of space, time and mass.
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:783
Tbl check_momentum_constraint(const Vector *momentum_density=0x0, ostream &ost=cout, bool verb=true) const
Checks the level at which the momentum constraints are verified.
int scheme_order
Order of the finite-differences scheme for the computation of time derivatives.
Definition: time_slice.h:190
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:393
Tensor up_down(const Metric &gam) const
Computes a new tensor by raising or lowering all the indices of *this .
Basic integer array class.
Definition: itbl.h:122
int jtime
Time step index of the latest slice.
Definition: time_slice.h:193
const Sym_tensor & ricci() const
Returns the Ricci tensor (given by the Connection p_connect )
Definition: metric.C:341
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
Definition: scalar_deriv.C:402
Tensor field of valence 1.
Definition: vector.h:188
virtual const Scalar & trk() const
Trace K of the extrinsic curvature at the current time step (jtime )
virtual const Sym_tensor & k_uu() const
Extrinsic curvature tensor (contravariant components ) at the current time step (jtime ) ...
const Vector & divergence(const Metric &) const
Returns the divergence of this with respect to a Metric .
Definition: sym_tensor.C:352
virtual const Scalar & ricci_scal() const
Returns the Ricci scalar.
Definition: metric.C:353
int get_index_type(int i) const
Gives the type (covariant or contravariant) of the index number i .
Definition: tensor.h:899
Evolution_std< Sym_tensor > k_dd_evol
Values at successive time steps of the covariant components of the extrinsic curvature tensor ...
Definition: time_slice.h:211
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:465
const Metric & gam() const
Induced metric at the current time step (jtime )
Tbl check_hamiltonian_constraint(const Scalar *energy_density=0x0, ostream &ost=cout, bool verb=true) const
Checks the level at which the hamiltonian constraint is verified.
int get_dim(int i) const
Gives the i-th dimension (ie dim.dim[i])
Definition: tbl.h:423
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
virtual const Sym_tensor & k_dd() const
Extrinsic curvature tensor (covariant components ) at the current time step (jtime ) ...
const Tensor & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of this with respect to some metric , by raising the last inde...
Definition: tensor.C:1023
virtual int position(const Itbl &ind) const
Returns the position in the array cmp of a component given by its indices.
Definition: tensor_sym.C:248
Basic array class.
Definition: tbl.h:164
const Map & get_mp() const
Returns the mapping.
Definition: tensor.h:874
void annule_hard()
Sets the Tbl to zero in a hard way.
Definition: tbl.C:375
virtual void dec_dzpuis(int dec=1)
Decreases by dec units the value of dzpuis and changes accordingly the values of the Scalar in the co...
Sym_tensor derive_lie(const Vector &v) const
Computes the Lie derivative of this with respect to some vector field v.
Definition: sym_tensor.C:363
Tbl check_dynamical_equations(const Sym_tensor *strain_tensor=0x0, const Scalar *energy_density=0x0, ostream &ost=cout, bool verb=true) const
Checks the level at which the dynamical equations are verified.
Class intended to describe valence-2 symmetric tensors.
Definition: sym_tensor.h:226
Tensor trace(int ind1, int ind2) const
Trace on two different type indices.
virtual const Scalar & nn() const
Lapse function N at the current time step (jtime )