et_rot_extr_curv.C

/*
 * Member function of class Etoile_rot to compute the extrinsic curvature
 */

/*
 *   Copyright (c) 2000-2001 Eric Gourgoulhon
 *
 *   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
 *
 */


char et_rot_extr_curv_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_extr_curv.C,v 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon Exp $" ;


/*
 * $Id: et_rot_extr_curv.C,v 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon Exp $
 * $Log: et_rot_extr_curv.C,v $
 * Revision 1.1.1.1  2001/11/20 15:19:28  e_gourgoulhon
 * LORENE
 *
 * Revision 2.2  2000/11/18  17:14:35  eric
 * Traitement du cas np=1 (axisymetrie).
 *
 * Revision 2.1  2000/10/06  15:07:10  eric
 * Traitement des cas ETATZERO.
 *
 * Revision 2.0  2000/09/18  16:15:45  eric
 * *** empty log message ***
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_extr_curv.C,v 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon Exp $
 *
 */

// Headers Lorene
#include "etoile.h"

void Etoile_rot::extrinsic_curvature(){
    

    // ---------------------------------------
    // Special treatment for axisymmetric case
    // ---------------------------------------
    
    if ( (mp.get_mg())->get_np(0) == 1) {
    
        tkij.set_etat_zero() ;      // initialisation
        
        
        // Computation of K_xy
        // -------------------
        
        Cmp dnpdr = nphi().dsdr() ;         // d/dr (N^phi)
        Cmp dnpdt = nphi().srdsdt() ;       // 1/r d/dtheta (N^phi)
        
        // What follows is valid only for a mapping of class Map_radial :   
        assert( dynamic_cast<const Map_radial*>(&mp) != 0x0 ) ;
        
        if (dnpdr.get_etat() == ETATQCQ) {
            dnpdr.va = (dnpdr.va).mult_st() ;   // multiplication by sin(theta)
        }
        
        if (dnpdt.get_etat() == ETATQCQ) {
            dnpdt.va = (dnpdt.va).mult_ct() ;   // multiplication by cos(theta)
        }
    
        Cmp tmp = dnpdr + dnpdt ;
    
        tmp.mult_rsint() ;          // multiplication by r sin(theta)
    
        if (tmp.get_etat() != ETATZERO) {
            tkij.set_etat_qcq() ;
            tkij.set(0,1) = - 0.5 * tmp / nnn() ;   // component (x,y)
        }
    
        // Computation of K_yz
        // -------------------
    
        dnpdr = nphi().dsdr() ;         // d/dr (N^phi)
        dnpdt = nphi().srdsdt() ;       // 1/r d/dtheta (N^phi)
        
        if (dnpdr.get_etat() == ETATQCQ) {
            dnpdr.va = (dnpdr.va).mult_ct() ;   // multiplication by cos(theta)
        }
        
        if (dnpdt.get_etat() == ETATQCQ) {
            dnpdt.va = (dnpdt.va).mult_st() ;   // multiplication by sin(theta)
        }
    
        tmp = dnpdr - dnpdt ;
        
        tmp.mult_rsint() ;          // multiplication by r sin(theta)
        
        if (tmp.get_etat() != ETATZERO) {
            if (tkij.get_etat() != ETATQCQ) {
                tkij.set_etat_qcq() ;
            }
            tkij.set(1,2) = - 0.5 * tmp / nnn() ;   // component (y,z)
        }
    
        // The other components are set to zero
        // ------------------------------------
        if (tkij.get_etat() == ETATQCQ) {
            tkij.set(0,0) = 0 ;         // component (x,x)
            tkij.set(0,2) = 0 ;         // component (x,z)
            tkij.set(1,1) = 0 ;         // component (y,y)
            tkij.set(2,2) = 0 ;         // component (z,z)
        }   
    
    
    
    }
    else {

    // ------------
    // General case
    // ------------

        // Gradient (Cartesian components) of the shift
        // D_j N^i
    
        Tenseur dn = shift.gradient() ;
    
        // Trace of D_j N^i = divergence of N^i :
        Tenseur divn = contract(dn, 0, 1) ;
    
        if (divn.get_etat() == ETATQCQ) {
    
            // Computation of B^{-2} K_{ij}
            // ----------------------------
            tkij.set_etat_qcq() ;
            for (int i=0; i<3; i++) {
                for (int j=i; j<3; j++) {
                    tkij.set(i, j) = dn(i, j) + dn(j, i)  ;
                }
                tkij.set(i, i) -= double(2) /double(3) * divn() ;
            }
    
            tkij = - 0.5 * tkij / nnn ;
    
        }
        else{
            assert( divn.get_etat() == ETATZERO ) ;
            tkij.set_etat_zero() ;
        }
    }
    
    // Computation of A^2 K_{ij} K^{ij}
    // --------------------------------
    
    if (tkij.get_etat() == ETATZERO) {
        ak_car = 0 ;
    }
    else {
        ak_car.set_etat_qcq() ;
    
        ak_car.set() = 0 ;
    
        for (int i=0; i<3; i++) {
            for (int j=0; j<3; j++) {
    
                ak_car.set() += tkij(i, j) * tkij(i, j) ;
    
            }
        }
    
        ak_car = b_car * ak_car ;
    }
    
}

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