LORENE
hole_bhns_rk_phi.C
1 /*
2  * Methods of class Hole_bhns to compute a forth-order Runge-Kutta
3  * integration to the phi direction for the solution of the Killing vectors
4  *
5  * (see file hole_bhns.h for documentation).
6  *
7  */
8 
9 /*
10  * Copyright (c) 2006-2007 Keisuke Taniguchi
11  *
12  * This file is part of LORENE.
13  *
14  * LORENE is free software; you can redistribute it and/or modify
15  * it under the terms of the GNU General Public License version 2
16  * as published by the Free Software Foundation.
17  *
18  * LORENE is distributed in the hope that it will be useful,
19  * but WITHOUT ANY WARRANTY; without even the implied warranty of
20  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21  * GNU General Public License for more details.
22  *
23  * You should have received a copy of the GNU General Public License
24  * along with LORENE; if not, write to the Free Software
25  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26  *
27  */
28 
29 char hole_bhns_rk_phi_C[] = "$Header: /cvsroot/Lorene/C++/Source/Hole_bhns/hole_bhns_rk_phi.C,v 1.4 2014/10/13 08:53:00 j_novak Exp $" ;
30 
31 /*
32  * $Id: hole_bhns_rk_phi.C,v 1.4 2014/10/13 08:53:00 j_novak Exp $
33  * $Log: hole_bhns_rk_phi.C,v $
34  * Revision 1.4 2014/10/13 08:53:00 j_novak
35  * Lorene classes and functions now belong to the namespace Lorene.
36  *
37  * Revision 1.3 2014/10/06 15:13:10 j_novak
38  * Modified #include directives to use c++ syntax.
39  *
40  * Revision 1.2 2008/07/02 20:47:55 k_taniguchi
41  * Typos removed.
42  *
43  * Revision 1.1 2008/05/15 19:10:31 k_taniguchi
44  * *** empty log message ***
45  *
46  *
47  * $Header: /cvsroot/Lorene/C++/Source/Hole_bhns/hole_bhns_rk_phi.C,v 1.4 2014/10/13 08:53:00 j_novak Exp $
48  *
49  */
50 
51 // C++ headers
52 //#include <>
53 
54 // C headers
55 #include <cmath>
56 
57 // Lorene headers
58 #include "hole_bhns.h"
59 #include "unites.h"
60 #include "utilitaires.h"
61 
62  //--------------------------------------------------//
63  // Forth-order Runge-Kutta on the equator //
64  //--------------------------------------------------//
65 
66 namespace Lorene {
67 Tbl Hole_bhns::runge_kutta_phi(const Tbl& xi_i, const double& phi_i,
68  const int& nrk_phi) const {
69 
70  using namespace Unites ;
71 
72  const Mg3d* mg = mp.get_mg() ;
73  int np = mg->get_np(1) ;
74 
75  Tbl xi_f(3) ; // xi_f(0)=xi_hat{theta}, xi_f(1)=xi_hat{phi}, xi_f(2)=L
76  xi_f.set_etat_qcq() ;
77 
78  if (kerrschild) {
79 
80  cout << "Not yet prepared!!!" << endl ;
81  abort() ;
82 
83  }
84  else { // Isotropic coordinates
85 
86  // Initial data at phi=0 on the equator
87  double xi_t0 = xi_i(0) ; // xi_hat{theta}
88  double xi_p0 = xi_i(1) ; // xi_hat{phi}
89  double xi_l0 = xi_i(2) ; // L
90  double phi0 = phi_i ;
91 
92  double dp = 2. * M_PI / double(np) / double(nrk_phi) ;
93 
94  double rah = rad_ah() ;
95 
96  Scalar dlnconfo(mp) ;
97  dlnconfo = confo_tot.dsdt() / confo_tot ;
98  dlnconfo.std_spectral_base() ;
99 
100  Scalar laplnconfo(mp) ;
101  laplnconfo = confo_tot.lapang() / confo_tot ;
102  laplnconfo.std_spectral_base() ;
103 
104  Scalar confo2(mp) ;
105  confo2 = confo_tot * confo_tot ;
106  confo2.std_spectral_base() ;
107 
108  double xi_t1, xi_t2, xi_t3, xi_t4, xi_tf ;
109  double xi_p1, xi_p2, xi_p3, xi_p4, xi_pf ;
110  double xi_l1, xi_l2, xi_l3, xi_l4, xi_lf ;
111  double f1, f2, f3, f4 ;
112  double g1, g2, g3, g4 ;
113  double h1, h2, h3, h4 ;
114 
115  // Forth-order Runge-Kutta
116  // (nrk_phi times steps between two collocation points)
117  // ----------------------------------------------------
118 
119  for (int i=0; i<nrk_phi; i++) {
120 
121  // First
122  f1 = - xi_l0 * rah * confo2.val_point(rah, M_PI/2., phi0)
123  + 2. * xi_p0 * dlnconfo.val_point(rah, M_PI/2., phi0) ;
124  g1 = -2. * xi_t0 * dlnconfo.val_point(rah, M_PI/2., phi0) ;
125  h1 = (1. - 2.*laplnconfo.val_point(rah, M_PI/2., phi0)) * xi_t0
126  / rah / confo2.val_point(rah, M_PI/2., phi0) ;
127 
128  xi_t1 = dp * f1 ;
129  xi_p1 = dp * g1 ;
130  xi_l1 = dp * h1 ;
131 
132  // Second
133  f2 = - (xi_l0+0.5*xi_l1) * rah
134  * confo2.val_point(rah, M_PI/2., phi0+0.5*dp)
135  + 2. * (xi_p0+0.5*xi_p1)
136  * dlnconfo.val_point(rah, M_PI/2., phi0+0.5*dp) ;
137  g2 = -2. * (xi_t0+0.5*xi_t1)
138  * dlnconfo.val_point(rah, M_PI/2., phi0+0.5*dp) ;
139  h2 = (1. - 2.*laplnconfo.val_point(rah, M_PI/2., phi0+0.5*dp))
140  * (xi_t0+0.5*xi_t1) / rah
141  / confo2.val_point(rah, M_PI/2., phi0+0.5*dp) ;
142 
143  xi_t2 = dp * f2 ;
144  xi_p2 = dp * g2 ;
145  xi_l2 = dp * h2 ;
146 
147  // Third
148  f3 = - (xi_l0+0.5*xi_l2) * rah
149  * confo2.val_point(rah, M_PI/2., phi0+0.5*dp)
150  + 2. * (xi_p0+0.5*xi_p2)
151  * dlnconfo.val_point(rah, M_PI/2., phi0+0.5*dp) ;
152  g3 = -2. * (xi_t0+0.5*xi_t2)
153  * dlnconfo.val_point(rah, M_PI/2., phi0+0.5*dp) ;
154  h3 = (1. - 2.*laplnconfo.val_point(rah, M_PI/2., phi0+0.5*dp))
155  * (xi_t0+0.5*xi_t2) / rah
156  / confo2.val_point(rah, M_PI/2., phi0+0.5*dp) ;
157 
158  xi_t3 = dp * f3 ;
159  xi_p3 = dp * g3 ;
160  xi_l3 = dp * h3 ;
161 
162  // Forth
163  f4 = - (xi_l0+xi_l3) * rah * confo2.val_point(rah, M_PI/2., phi0+dp)
164  + 2. * (xi_p0+xi_p3) * dlnconfo.val_point(rah, M_PI/2., phi0+dp) ;
165  g4 = -2. * (xi_t0+xi_t3) * dlnconfo.val_point(rah, M_PI/2., phi0+dp) ;
166  h4 = (1. - 2.*laplnconfo.val_point(rah, M_PI/2., phi0+dp))
167  * (xi_t0+xi_t3) / rah / confo2.val_point(rah, M_PI/2., phi0+dp) ;
168 
169  xi_t4 = dp * f4 ;
170  xi_p4 = dp * g4 ;
171  xi_l4 = dp * h4 ;
172 
173  // Final results
174  // -------------
175  xi_tf = xi_t0 + (xi_t1 + 2.*xi_t2 + 2.*xi_t3 + xi_t4) / 6. ;
176  xi_pf = xi_p0 + (xi_p1 + 2.*xi_p2 + 2.*xi_p3 + xi_p4) / 6. ;
177  xi_lf = xi_l0 + (xi_l1 + 2.*xi_l2 + 2.*xi_l3 + xi_l4) / 6. ;
178 
179  // Final results are put into the initial data
180  // in order for the next step
181  // -------------------------------------------
182  xi_t0 = xi_tf ;
183  xi_p0 = xi_pf ;
184  xi_l0 = xi_lf ;
185 
186  } // End of the loop
187 
188  xi_f.set(0) = xi_tf ;
189  xi_f.set(1) = xi_pf ;
190  xi_f.set(2) = xi_lf ;
191 
192  }
193 
194  return xi_f ;
195 
196 }
197 }
Map & mp
Mapping associated with the black hole.
Definition: blackhole.h:80
const Scalar & lapang() const
Returns the angular Laplacian of *this , where .
Definition: scalar_deriv.C:461
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition: grilles.h:462
Lorene prototypes.
Definition: app_hor.h:64
Standard units of space, time and mass.
const Scalar & dsdt() const
Returns of *this .
Definition: scalar_deriv.C:208
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition: tbl.h:281
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:387
bool kerrschild
true for a Kerr-Schild background, false for a conformally flat background
Definition: blackhole.h:85
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field. ...
Definition: scalar.C:784
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tbl.C:361
virtual double rad_ah() const
Radius of the apparent horizon.
double val_point(double r, double theta, double phi) const
Computes the value of the field at an arbitrary point , by means of the spectral expansion.
Definition: scalar.C:890
Tbl runge_kutta_phi(const Tbl &xi_i, const double &phi_i, const int &nrk) const
Compute a forth-order Runge-Kutta integration to the phi direction for the solution of the Killing ve...
Scalar confo_tot
Total conformal factor.
Definition: hole_bhns.h:169
Multi-domain grid.
Definition: grilles.h:273
Basic array class.
Definition: tbl.h:161