vector_poisson_boundary.C
/*
* Method for vector Poisson equation inverting eqs. for V^r and eta as a block
* (with a boundary condition on the excised sphere).
*
* (see file vector.h for documentation).
*
*/
/*
* Copyright (c) 2005 Jerome Novak
* Francois Limousin
* Jose Luis Jaramillo
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2
* as published by the Free Software Foundation.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
char vector_poisson_boundary_C[] = "$Header: /cvsroot/Lorene/C++/Source/Tensor/vector_poisson_boundary.C,v 1.3 2014/10/13 08:53:45 j_novak Exp $" ;
/*
* $Id: vector_poisson_boundary.C,v 1.3 2014/10/13 08:53:45 j_novak Exp $
* $Log: vector_poisson_boundary.C,v $
* Revision 1.3 2014/10/13 08:53:45 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.2 2014/10/06 15:13:21 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.1 2005/06/09 08:00:09 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.
*
*
* $Header: /cvsroot/Lorene/C++/Source/Tensor/vector_poisson_boundary.C,v 1.3 2014/10/13 08:53:45 j_novak Exp $
*
*/
// C headers
#include <cassert>
#include <cstdlib>
#include <cmath>
// Lorene headers
#include "metric.h"
#include "diff.h"
#include "param_elliptic.h"
#include "proto.h"
#include "utilitaires.h"
namespace Lorene {
void Vector::poisson_boundary(double lam, const Mtbl_cf& bound_vr,
const Mtbl_cf& bound_eta, const Mtbl_cf& bound_mu,
int num_front, double fact_dir, double fact_neu,
Vector& resu) const {
const Map_af* mpaff = dynamic_cast<const Map_af*>(mp) ;
#ifndef NDEBUG
for (int i=0; i<3; i++)
assert(cmp[i]->check_dzpuis(4)) ;
// All this has a meaning only for spherical components:
const Base_vect_spher* bvs = dynamic_cast<const Base_vect_spher*>(triad) ;
assert(bvs != 0x0) ;
//## ... and affine mapping, for the moment!
assert( mpaff != 0x0) ;
#endif
if (fabs(lam + 1.) < 1.e-8) {
cout << "Not implemented yet !!" << endl ;
abort() ;
/*
const Metric_flat& mets = mp->flat_met_spher() ;
Vector_divfree sou(*mp, *triad, mets) ;
for (int i=1; i<=3; i++) sou.set(i) = *cmp[i-1] ;
resu = sou.poisson() ;
return ;
*/
}
// Some working objects
//---------------------
const Mg3d& mg = *mpaff->get_mg() ;
int nz = mg.get_nzone() ; int nzm1 = nz - 1;
assert(mg.get_type_r(nzm1) == UNSURR) ;
Scalar S_r = *cmp[0] ;
if (S_r.get_etat() == ETATZERO) S_r.annule_hard() ;
Scalar S_eta = eta() ;
if (S_eta.get_etat() == ETATZERO) S_eta.annule_hard() ;
S_r.set_spectral_va().ylm() ;
S_eta.set_spectral_va().ylm() ;
const Base_val& base = S_eta.get_spectral_va().base ;
Mtbl_cf sol_part_eta(mg, base) ; sol_part_eta.annule_hard() ;
Mtbl_cf sol_part_vr(mg, base) ; sol_part_vr.annule_hard() ;
Mtbl_cf solution_hom_un(mg, base) ; solution_hom_un.annule_hard() ;
Mtbl_cf solution_hom_deux(mg, base) ; solution_hom_deux.annule_hard() ;
Mtbl_cf solution_hom_trois(mg, base) ; solution_hom_trois.annule_hard() ;
Mtbl_cf solution_hom_quatre(mg, base) ; solution_hom_quatre.annule_hard() ;
// The l_0 component is solved independently // Understand this step
//------------------------------------------
Scalar sou_l0 = (*cmp[0]) / (1. + lam) ;
Param_elliptic param_l0(sou_l0) ;
for (int l=0; l<nz; l++)
param_l0.set_poisson_vect_r(l, true) ;
// Scalar vrl0 = sou_l0.sol_elliptic(param_l0) ;
Scalar vrl0 = sou_l0.sol_elliptic_boundary(param_l0, bound_vr, fact_dir, fact_neu) ;
// Build-up & inversion of the system for (eta, V^r) in each domain
//-----------------------------------------------------------------
// Shells
//-------
int nr ;
int nt = mg.get_nt(0) ;
int np = mg.get_np(0) ;
int l_q = 0 ; int m_q = 0; int base_r = 0 ;
double alpha, beta, ech ;
assert(num_front+1 < nzm1) ; // Minimum one shell
for (int zone=num_front+1 ; zone<nzm1 ; zone++) { //begins the loop on zones
nr = mg.get_nr(zone) ;
alpha = mpaff->get_alpha()[zone] ;
beta = mpaff->get_beta()[zone] ;
ech = beta / alpha ;
assert (nr > 5) ;
assert(nt == mg.get_nt(zone)) ;
assert(np == mg.get_np(zone)) ;
// Loop on l and m
//----------------
for (int k=0 ; k<np+1 ; k++) {
for (int j=0 ; j<nt ; j++) {
base.give_quant_numbers(zone, k, j, m_q, l_q, base_r) ;
if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q != 0) ) {
int dege1 = 2 ; //degeneracy of eq.1
int dege2 = 2 ; //degeneracy of eq.2
int nr_eq1 = nr - dege1 ; //Eq.1 is for eta
int nr_eq2 = nr - dege2 ; //Eq.2 is for V^r
int nrtot = nr_eq1 + nr_eq2 ;
Matrice oper(nrtot, nrtot) ; oper.set_etat_qcq() ;
Tbl sec_membre(nrtot) ; sec_membre.set_etat_qcq() ;
Diff_x2dsdx2 x2d2(base_r, nr); const Matrice& m2d2 = x2d2.get_matrice() ;
Diff_xdsdx2 xd2(base_r, nr) ; const Matrice& mxd2 = xd2.get_matrice() ;
Diff_dsdx2 d2(base_r, nr) ; const Matrice& md2 = d2.get_matrice() ;
Diff_xdsdx xd(base_r, nr) ; const Matrice& mxd = xd.get_matrice() ;
Diff_dsdx d1(base_r, nr) ; const Matrice& md = d1.get_matrice() ;
Diff_id id(base_r, nr) ; const Matrice& mid = id.get_matrice() ;
// Building the operator // Which is the eq. from the notes that it is actually implemented?
//----------------------
for (int lin=0; lin<nr_eq1; lin++) {
for (int col=dege1; col<nr; col++)
oper.set(lin,col-dege1)
= m2d2(lin,col) + 2*ech*mxd2(lin,col) + ech*ech*md2(lin,col)
+ 2*(mxd(lin,col) + ech*md(lin,col))
- (lam+1)*l_q*(l_q+1)*mid(lin,col) ;
for (int col=dege2; col<nr; col++)
oper.set(lin,col-dege2+nr_eq1)
= lam*(mxd(lin,col) + ech*md(lin,col)) + 2*(1+lam)*mid(lin,col) ;
}
for (int lin=0; lin<nr_eq2; lin++) {
for (int col=dege1; col<nr; col++)
oper.set(lin+nr_eq1,col-dege1)
= -l_q*(l_q+1)*(lam*(mxd(lin,col) + ech*md(lin,col))
- (lam+2)*mid(lin,col)) ;
for (int col=dege2; col<nr; col++)
oper.set(lin+nr_eq1, col-dege2+nr_eq1)
= (lam+1)*(m2d2(lin,col) + 2*ech*mxd2(lin,col)
+ ech*ech*md2(lin,col)
+ 2*(mxd(lin,col) + ech*md(lin,col)))
-(2*(lam+1)+l_q*(l_q+1))*mid(lin,col) ;
}
oper.set_lu() ;
// Filling the r.h.s
//------------------
Tbl sr(nr) ; sr.set_etat_qcq() ;
Tbl seta(nr) ; seta.set_etat_qcq() ;
for (int i=0; i<nr; i++) {
sr.set(i) = (*S_r.get_spectral_va().c_cf)(zone, k, j, i);
seta.set(i) = (*S_eta.get_spectral_va().c_cf)(zone, k, j, i) ;
}
Tbl xsr= sr ; Tbl x2sr= sr ;
Tbl xseta= seta ; Tbl x2seta = seta ;
multx2_1d(nr, &x2sr.t, base_r) ; multx_1d(nr, &xsr.t, base_r) ;
multx2_1d(nr, &x2seta.t, base_r) ; multx_1d(nr, &xseta.t, base_r) ;
for (int i=0; i<nr_eq1; i++)
sec_membre.set(i) = alpha*(alpha*x2seta(i) + 2*beta*xseta(i))
+ beta*beta*seta(i);
for (int i=0; i<nr_eq2; i++)
sec_membre.set(i+nr_eq1) = beta*beta*sr(i)
+ alpha*(alpha*x2sr(i) + 2*beta*xsr(i)) ;
// Inversion of the "big" operator
//--------------------------------
Tbl big_res = oper.inverse(sec_membre) ;
Tbl res_eta(nr) ; res_eta.set_etat_qcq() ;
Tbl res_vr(nr) ; res_vr.set_etat_qcq() ;
// Putting coefficients of h and v to individual arrays
//-----------------------------------------------------
for (int i=0; i<dege1; i++)
res_eta.set(i) = 0 ;
for (int i=dege1; i<nr; i++)
res_eta.set(i) = big_res(i-dege1) ;
for (int i=0; i<dege2; i++)
res_vr.set(i) = 0 ;
for (int i=dege2; i<nr; i++)
res_vr.set(i) = big_res(i-dege2+nr_eq1) ;
//homogeneous solutions //I do not understand!!!
Tbl sol_hom1 = solh(nr, l_q-1, ech, base_r) ;
Tbl sol_hom2 = solh(nr, l_q+1, ech, base_r) ;
for (int i=0 ; i<nr ; i++) {
sol_part_eta.set(zone, k, j, i) = res_eta(i) ;
sol_part_vr.set(zone, k, j, i) = res_vr(i) ;
solution_hom_un.set(zone, k, j, i) = sol_hom1(0,i) ;
solution_hom_deux.set(zone, k, j, i) = sol_hom2(1,i) ;
solution_hom_trois.set(zone, k, j, i) = sol_hom2(0,i) ;
solution_hom_quatre.set(zone, k, j, i) = sol_hom1(1,i) ;
}
}
}
}
}
// Compactified external domain
//-----------------------------
nr = mg.get_nr(nzm1) ;
assert(nt == mg.get_nt(nzm1)) ;
assert(np == mg.get_np(nzm1)) ;
alpha = mpaff->get_alpha()[nzm1] ;
assert (nr > 4) ;
int nr0 = nr - 2 ; //two degrees of freedom less because of division by u^2
// Loop on l and m
//----------------
for (int k=0 ; k<np+1 ; k++) {
for (int j=0 ; j<nt ; j++) {
base.give_quant_numbers(nzm1, k, j, m_q, l_q, base_r) ;
if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q != 0) ) {
int dege1 = 1; //degeneracy of eq.1
int dege2 = 0; //degeneracy of eq.2
int nr_eq1 = nr0 - dege1 ; //Eq.1 is for eta
int nr_eq2 = nr0 - dege2 ; //Eq.2 is the div-free condition
int nrtot = nr_eq1 + nr_eq2 ;
Matrice oper(nrtot, nrtot) ; oper.set_etat_qcq() ;
Tbl sec_membre(nrtot) ; sec_membre.set_etat_qcq() ;
Diff_x2dsdx2 x2d2(base_r, nr) ; const Matrice& m2d2 = x2d2.get_matrice() ;
Diff_xdsdx xd(base_r, nr) ; const Matrice& mxd = xd.get_matrice() ;
Diff_id id(base_r, nr) ; const Matrice& mid = id.get_matrice() ;
// Building the operator
//----------------------
for (int lin=0; lin<nr_eq1; lin++) {
for (int col=dege1; col<nr0; col++)
oper.set(lin,col-dege1)
= m2d2(lin,col) + 4*mxd(lin,col)
+ (2-(lam+1)*l_q*(l_q+1))*mid(lin,col) ;
for (int col=dege2; col<nr0; col++)
oper.set(lin,col-dege2+nr_eq1) =
-lam*mxd(lin,col) + 2*mid(lin,col) ;
}
for (int lin=0; lin<nr_eq2; lin++) {
for (int col=dege1; col<nr0; col++)
oper.set(lin+nr_eq1,col-dege1)
= l_q*(l_q+1)*(lam*mxd(lin,col) + (3*lam+2)*mid(lin,col)) ;
for (int col=dege2; col<nr0; col++)
oper.set(lin+nr_eq1, col-dege2+nr_eq1)
= (lam+1)*(m2d2(lin,col) + 4*mxd(lin,col))
- l_q*(l_q+1)*mid(lin,col) ;
}
oper.set_lu() ;
// Filling the r.h.s
//------------------
for (int i=0; i<nr_eq1; i++)
sec_membre.set(i) = (*S_eta.get_spectral_va().c_cf)(nzm1, k, j, i) ;
for (int i=0; i<nr_eq2; i++)
sec_membre.set(i+nr_eq1) =(*S_r.get_spectral_va().c_cf)(nzm1, k, j, i);
Tbl big_res = oper.inverse(sec_membre) ;
Tbl res_eta(nr) ; res_eta.set_etat_qcq() ;
Tbl res_vr(nr) ; res_vr.set_etat_qcq() ;
// Putting coefficients of h and v to individual arrays
//-----------------------------------------------------
for (int i=0; i<dege1; i++)
res_eta.set(i) = 0 ;
for (int i=dege1; i<nr0; i++)
res_eta.set(i) = big_res(i-dege1) ;
res_eta.set(nr0) = 0 ;
res_eta.set(nr0+1) = 0 ;
for (int i=0; i<dege2; i++)
res_vr.set(i) = 0 ;
for (int i=dege2; i<nr0; i++)
res_vr.set(i) = big_res(i-dege2+nr_eq1) ;
res_vr.set(nr0) = 0 ;
res_vr.set(nr0+1) = 0 ;
// Multiplication by u^2
//-----------------------
Tbl res_v2(nr) ; res_v2.set_etat_qcq() ;
Tbl res_e2(nr) ; res_e2.set_etat_qcq() ;
mult2_xm1_1d_cheb(nr, res_eta.t, res_e2.t) ;
mult2_xm1_1d_cheb(nr, res_vr.t, res_v2.t) ;
// Homogeneous solution (only 1/r^(l+2) and 1/r^l in the CED)
Tbl sol_hom1 = solh(nr, l_q-1, 0., base_r) ;
Tbl sol_hom2 = solh(nr, l_q+1, 0., base_r) ;
for (int i=0 ; i<nr ; i++) {
sol_part_eta.set(nzm1, k, j, i) = alpha*alpha*res_e2(i) ;
sol_part_vr.set(nzm1, k, j, i) = alpha*alpha*res_v2(i) ;
solution_hom_un.set(nzm1, k, j, i) = 0. ;
solution_hom_deux.set(nzm1, k, j, i) = sol_hom2(i) ;
solution_hom_trois.set(nzm1, k, j, i) = 0. ;
solution_hom_quatre.set(nzm1, k, j, i) = sol_hom1(i) ;
}
}
}
}
// Now let's match everything ...
//-------------------------------
// Resulting V^r & eta
Scalar vr(*mpaff) ; vr.set_etat_qcq() ;
vr.set_spectral_base(base) ;
vr.set_spectral_va().set_etat_cf_qcq() ;
Mtbl_cf& cf_vr = *vr.set_spectral_va().c_cf ;
cf_vr.annule_hard() ;
Scalar het(*mpaff) ; het.set_etat_qcq() ;
het.set_spectral_base(base) ;
het.set_spectral_va().set_etat_cf_qcq() ;
Mtbl_cf& cf_eta = *het.set_spectral_va().c_cf ;
cf_eta.annule_hard() ;
int taille = 4*(nzm1-num_front)-2 ; //## a verifier
Tbl sec_membre(taille) ;
Matrice systeme(taille, taille) ;
systeme.set_etat_qcq() ;
int ligne ; int colonne ;
// Loop on l and m
//----------------
for (int k=0 ; k<np+1 ; k++)
for (int j=0 ; j<nt ; j++) {
base.give_quant_numbers(0, k, j, m_q, l_q, base_r) ;
if ((nullite_plm(j, nt, k, np, base) == 1)&&(l_q != 0)) {
double f3_eta = lam*l_q + 3*lam + 2 ;
double f4_eta = 2 + 2*lam - lam*l_q ;
double f3_vr = (l_q+1)*(lam*l_q - 2) ;
double f4_vr = l_q*(lam*l_q + lam + 2) ;
ligne = 0 ;
colonne = 0 ;
sec_membre.annule_hard() ;
for (int l=0; l<taille; l++)
for (int c=0; c<taille; c++)
systeme.set(l,c) = 0 ;
// First shell
nr = mg.get_nr(num_front+1) ;
alpha = mpaff->get_alpha()[num_front+1] ;
double echelle = mpaff->get_beta()[num_front+1]/alpha ;
// Conditions on eta (configuration space)
//value and derivative of (x+echelle)^(l-1) at -1
systeme.set(ligne, colonne) = pow(echelle-1., double(l_q-1)) ;
// value and derivative of 1/(x+echelle) ^(l+2) at -1
systeme.set(ligne, colonne+1) = 1/pow(echelle-1., double(l_q+2)) ;
//value and derivative of (x+echelle)^(l+1) at -1
systeme.set(ligne, colonne+2) = f3_eta*pow(echelle-1., double(l_q+1)) ;
// value and derivative of 1/(x+echelle) ^l at -1
systeme.set(ligne, colonne+3) = f4_eta/pow(echelle-1., double(l_q)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0)
sec_membre.set(ligne) -= sol_part_eta(num_front+1, k, j, i) ;
else sec_membre.set(ligne) += sol_part_eta(num_front+1, k, j, i) ;
sec_membre.set(ligne) += bound_eta(num_front+1, k, j, 0) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne) = fact_dir*l_q*pow(echelle-1., double(l_q-1)) + fact_neu*l_q*(l_q-1)*pow(echelle-1., double(l_q-2))/alpha ;
systeme.set(ligne, colonne+1) = -fact_dir*(l_q+1)/pow(echelle-1., double(l_q+2)) + fact_neu*(l_q+1)*(l_q+2)/pow(echelle-1., double(l_q+3))/alpha ;
systeme.set(ligne, colonne+2) = fact_dir*f3_vr*pow(echelle-1., double(l_q+1)) + fact_neu*f3_vr*(l_q+1)*pow(echelle-1., double(l_q))/alpha ;
systeme.set(ligne, colonne+3) = fact_dir*f4_vr/pow(echelle-1., double(l_q)) - fact_neu*(f4_vr*l_q/pow(echelle-1., double(l_q+1)))/alpha ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0)
sec_membre.set(ligne) -= fact_dir*sol_part_vr(num_front+1, k, j, i) - fact_neu*i*i/alpha*sol_part_vr(num_front+1, k, j, i) ;
else sec_membre.set(ligne) += fact_dir*sol_part_vr(num_front+1, k, j, i) - fact_neu*i*i/alpha*sol_part_vr(num_front+1, k, j, i) ;
sec_membre.set(ligne) += bound_vr(num_front+1, k, j, 0) ;
ligne++ ;
// Values at 1
// eta
//value of (x+echelle)^(l-1) at 1
systeme.set(ligne, colonne) = pow(echelle+1., double(l_q-1)) ;
// value of 1/(x+echelle) ^(l+2) at 1
systeme.set(ligne, colonne+1) = 1./pow(echelle+1., double(l_q+2)) ;
//value of (x+echelle)^(l+1) at 1
systeme.set(ligne, colonne+2) = f3_eta*pow(echelle+1., double(l_q+1));
// value of 1/(x+echelle) ^l at 1
systeme.set(ligne, colonne+3) = f4_eta/pow(echelle+1., double(l_q)) ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= sol_part_eta(num_front+1, k, j, i) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne) = l_q*pow(echelle+1., double(l_q-1)) ;
systeme.set(ligne, colonne+1)
= -double(l_q+1) / pow(echelle+1., double(l_q+2));
systeme.set(ligne, colonne+2) = f3_vr*pow(echelle+1., double(l_q+1)) ;
systeme.set(ligne, colonne+3) = f4_vr/pow(echelle+1., double(l_q));
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= sol_part_vr(num_front+1, k, j, i) ;
ligne++ ;
//Derivatives at 1
// eta
//derivative of (x+echelle)^(l-1) at 1
systeme.set(ligne, colonne)
= (l_q-1) * pow(echelle+1., double(l_q-2))/alpha ;
// derivative of 1/(x+echelle) ^(l+2) at 1
systeme.set(ligne, colonne+1)
= -(l_q+2) / pow(echelle+1., double(l_q+3))/alpha ;
// derivative of (x+echelle)^(l+1) at 1
systeme.set(ligne, colonne+2)
= f3_eta*(l_q+1) * pow(echelle+1., double(l_q))/alpha;
// derivative of 1/(x+echelle) ^l at 1
systeme.set(ligne, colonne+3)
= -f4_eta*l_q / pow(echelle+1., double(l_q+1))/alpha ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= i*i/alpha*sol_part_eta(num_front+1, k, j, i) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne)
= l_q*(l_q-1) * pow(echelle+1., double(l_q-2))/alpha ;
systeme.set(ligne, colonne+1)
= (l_q+1)*(l_q+2) / pow(echelle+1., double(l_q+3))/alpha ;
systeme.set(ligne, colonne+2)
= f3_vr*(l_q+1) * pow(echelle+1., double(l_q))/alpha ;
systeme.set(ligne, colonne+3)
= -f4_vr*l_q / pow(echelle+1., double(l_q+1))/alpha ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= i*i/alpha*sol_part_vr(num_front+1, k, j, i) ;
colonne += 4 ; // We pass to the next domain
// Next shells
if (num_front+2<nzm1){
for (int zone=num_front+2 ; zone<nzm1 ; zone++) {
nr = mg.get_nr(zone) ;
alpha = mpaff->get_alpha()[zone] ;
echelle = mpaff->get_beta()[zone]/alpha ;
ligne -= 3 ;
//value of (x+echelle)^(l-1) at -1
systeme.set(ligne, colonne) = -pow(echelle-1., double(l_q-1)) ;
// value of 1/(x+echelle) ^(l+2) at -1
systeme.set(ligne, colonne+1) = -1/pow(echelle-1., double(l_q+2)) ;
//value of (x+echelle)^(l+1) at -1
systeme.set(ligne, colonne+2) = -f3_eta*pow(echelle-1., double(l_q+1));
// value of 1/(x+echelle) ^l at -1
systeme.set(ligne, colonne+3) = -f4_eta/pow(echelle-1., double(l_q)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0)
sec_membre.set(ligne) += sol_part_eta(zone, k, j, i) ;
else sec_membre.set(ligne) -= sol_part_eta(zone, k, j, i) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne) = -l_q*pow(echelle-1., double(l_q-1)) ;
systeme.set(ligne, colonne+1) = (l_q+1)/pow(echelle-1., double(l_q+2));
systeme.set(ligne, colonne+2) = -f3_vr*pow(echelle-1., double(l_q+1)) ;
systeme.set(ligne, colonne+3) = -f4_vr/pow(echelle-1., double(l_q));
for (int i=0 ; i<nr ; i++)
if (i%2 == 0)
sec_membre.set(ligne) += sol_part_vr(zone, k, j, i) ;
else sec_membre.set(ligne) -= sol_part_vr(zone, k, j, i) ;
ligne++ ;
//derivative of (x+echelle)^(l-1) at -1
systeme.set(ligne, colonne)
= -(l_q-1)*pow(echelle-1., double(l_q-2))/alpha ;
// derivative of 1/(x+echelle) ^(l+2) at -1
systeme.set(ligne, colonne+1)
= (l_q+2)/pow(echelle-1., double(l_q+3))/alpha ;
// derivative of (x+echelle)^(l+1) at -1
systeme.set(ligne, colonne+2)
= -f3_eta*(l_q+1)*pow(echelle-1., double(l_q))/alpha;
// derivative of 1/(x+echelle) ^l at -1
systeme.set(ligne, colonne+3)
= (f4_eta*l_q/pow(echelle-1., double(l_q+1)))/alpha ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne)
-= i*i/alpha*sol_part_eta(zone, k, j, i) ;
else sec_membre.set(ligne) +=
i*i/alpha*sol_part_eta(zone, k, j, i) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne)
= -l_q*(l_q-1)*pow(echelle-1., double(l_q-2))/alpha ;
systeme.set(ligne, colonne+1)
= -(l_q+1)*(l_q+2)/pow(echelle-1., double(l_q+3))/alpha ;
systeme.set(ligne, colonne+2)
= -f3_vr*(l_q+1)*pow(echelle-1., double(l_q))/alpha ;
systeme.set(ligne, colonne+3)
= (f4_vr*l_q/pow(echelle-1., double(l_q+1)))/alpha ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne)
-= i*i/alpha*sol_part_vr(zone, k, j, i) ;
else sec_membre.set(ligne) +=
i*i/alpha*sol_part_vr(zone, k, j, i) ;
ligne++ ;
//value of (x+echelle)^(l-1) at 1
systeme.set(ligne, colonne) = pow(echelle+1., double(l_q-1)) ;
// value of 1/(x+echelle) ^(l+2) at 1
systeme.set(ligne, colonne+1) = 1./pow(echelle+1., double(l_q+2)) ;
//value of (x+echelle)^(l+1) at 1
systeme.set(ligne, colonne+2) = f3_eta*pow(echelle+1., double(l_q+1));
// value of 1/(x+echelle) ^l at 1
systeme.set(ligne, colonne+3) = f4_eta/pow(echelle+1., double(l_q)) ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= sol_part_eta(zone, k, j, i) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne) = l_q*pow(echelle+1., double(l_q-1)) ;
systeme.set(ligne, colonne+1)
= -double(l_q+1) / pow(echelle+1., double(l_q+2));
systeme.set(ligne, colonne+2) = f3_vr*pow(echelle+1., double(l_q+1)) ;
systeme.set(ligne, colonne+3) = f4_vr/pow(echelle+1., double(l_q));
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= sol_part_vr(zone, k, j, i) ;
ligne++ ;
//derivative of (x+echelle)^(l-1) at 1
systeme.set(ligne, colonne)
= (l_q-1) * pow(echelle+1., double(l_q-2))/alpha ;
// derivative of 1/(x+echelle) ^(l+2) at 1
systeme.set(ligne, colonne+1)
= -(l_q+2) / pow(echelle+1., double(l_q+3))/alpha ;
// derivative of (x+echelle)^(l+1) at 1
systeme.set(ligne, colonne+2)
= f3_eta*(l_q+1) * pow(echelle+1., double(l_q))/alpha;
// derivative of 1/(x+echelle) ^l at 1
systeme.set(ligne, colonne+3)
= -f4_eta*l_q / pow(echelle+1., double(l_q+1))/alpha ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= i*i/alpha*sol_part_eta(zone, k, j, i) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne)
= l_q*(l_q-1) * pow(echelle+1., double(l_q-2))/alpha ;
systeme.set(ligne, colonne+1)
= (l_q+1)*(l_q+2) / pow(echelle+1., double(l_q+3))/alpha ;
systeme.set(ligne, colonne+2)
= f3_vr*(l_q+1) * pow(echelle+1., double(l_q))/alpha ;
systeme.set(ligne, colonne+3)
= -f4_vr*l_q / pow(echelle+1., double(l_q+1))/alpha ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= i*i/alpha*sol_part_vr(zone, k, j, i) ;
colonne += 4 ;
}
}
//Compactified external domain
nr = mg.get_nr(nzm1) ;
alpha = mpaff->get_alpha()[nzm1] ;
ligne -= 3 ;
//value of (x-1)^(l+2) at -1 :
systeme.set(ligne, colonne) = -pow(-2, double(l_q+2)) ;
//value of (x-1)^l at -1 :
systeme.set(ligne, colonne+1) = -f4_eta*pow(-2, double(l_q)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne) += sol_part_eta(nzm1, k, j, i) ;
else sec_membre.set(ligne) -= sol_part_eta(nzm1, k, j, i) ;
//... and of its couterpart for V^r
systeme.set(ligne+1, colonne) = double(l_q+1)*pow(-2, double(l_q+2)) ;
systeme.set(ligne+1, colonne+1) = -f4_vr*pow(-2, double(l_q)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne+1) += sol_part_vr(nzm1, k, j, i) ;
else sec_membre.set(ligne+1) -= sol_part_vr(nzm1, k, j, i) ;
ligne += 2 ;
//derivative of (x-1)^(l+2) at -1 :
systeme.set(ligne, colonne) = alpha*(l_q+2)*pow(-2, double(l_q+3)) ;
//derivative of (x-1)^l at -1 :
systeme.set(ligne, colonne+1) = alpha*l_q*f4_eta*pow(-2, double(l_q+1)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne)
-= -4*alpha*i*i*sol_part_eta(nzm1, k, j, i) ;
else sec_membre.set(ligne)
+= -4*alpha*i*i*sol_part_eta(nzm1, k, j, i) ;
//... and of its couterpart for V^r
systeme.set(ligne+1, colonne)
= -alpha*double((l_q+1)*(l_q+2))*pow(-2, double(l_q+3)) ;
systeme.set(ligne+1, colonne+1)
= alpha*double(l_q)*f4_vr*pow(-2, double(l_q+1)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne+1)
-= -4*alpha*i*i*sol_part_vr(nzm1, k, j, i) ;
else sec_membre.set(ligne+1)
+= -4*alpha*i*i*sol_part_vr(nzm1, k, j, i) ;
// Solution of the system giving the coefficients for the homogeneous
// solutions
//-------------------------------------------------------------------
if (taille > 2) systeme.set_band(5,5) ;
else systeme.set_band(1,1) ;
systeme.set_lu() ;
Tbl facteurs(systeme.inverse(sec_membre)) ;
int conte = 0 ;
// everything is put to the right place, the same combination of hom.
// solutions (with some l or -(l+1) factors) must be used for V^r
//-------------------------------------------------------------------
for (int zone=1 ; zone<nzm1 ; zone++) { //shells
nr = mg.get_nr(zone) ;
for (int i=0 ; i<nr ; i++) {
cf_eta.set(zone, k, j, i) =
sol_part_eta(zone, k, j, i)
+facteurs(conte)*solution_hom_un(zone, k, j, i)
+facteurs(conte+1)*solution_hom_deux(zone, k, j, i)
+facteurs(conte+2)*f3_eta*solution_hom_trois(zone, k, j, i)
+facteurs(conte+3)*f4_eta*solution_hom_quatre(zone, k, j, i) ;
cf_vr.set(zone, k, j, i) = sol_part_vr(zone, k, j, i)
+double(l_q)*facteurs(conte)*solution_hom_un(zone, k, j, i)
-double(l_q+1)*facteurs(conte+1)*solution_hom_deux(zone, k, j, i) // What is the origin of these factors?!
+f3_vr*facteurs(conte+2)*solution_hom_trois(zone, k, j, i)
+f4_vr*facteurs(conte+3)*solution_hom_quatre(zone, k, j, i) ;
}
conte+=4 ;
}
nr = mg.get_nr(nz-1) ; //compactified external domain
for (int i=0 ; i<nr ; i++) {
cf_eta.set(nzm1, k, j, i) = sol_part_eta(nzm1, k, j, i)
+facteurs(conte)*solution_hom_deux(nzm1, k, j, i)
+f4_eta*facteurs(conte+1)*solution_hom_quatre(nzm1, k, j, i) ;
cf_vr.set(nzm1, k, j, i) = sol_part_vr(nzm1, k, j, i)
-double(l_q+1)*facteurs(conte)*solution_hom_deux(nzm1, k, j, i)
+f4_vr*facteurs(conte+1)*solution_hom_quatre(nzm1, k, j, i) ;
}
} // End of nullite_plm
} //End of loop on theta
vr.set_spectral_va().ylm_i() ;
vr += vrl0 ;
het.set_spectral_va().ylm_i() ;
Valeur temp_mu(mg.get_angu()) ;
temp_mu = bound_mu ;
const Valeur& limit_mu (temp_mu) ;
resu.set_vr_eta_mu(vr, 0*het, mu().poisson_dirichlet(limit_mu, num_front)) ;
return ;
}
Vector Vector::poisson_dirichlet(double lam, const Valeur& bound_vr,
const Valeur& bound_vt, const Valeur& bound_vp,
int num_front) const {
Vector resu(*mp, CON, triad) ;
resu = poisson_robin(lam, bound_vr, bound_vt, bound_vp, 1., 0., num_front) ;
return resu ;
}
Vector Vector::poisson_neumann(double lam, const Valeur& bound_vr,
const Valeur& bound_vt, const Valeur& bound_vp,
int num_front) const {
Vector resu(*mp, CON, triad) ;
resu = poisson_robin(lam, bound_vr, bound_vt, bound_vp, 0., 1., num_front) ;
return resu ;
}
Vector Vector::poisson_robin(double lam, const Valeur& bound_vr,
const Valeur& bound_vt, const Valeur& bound_vp,
double fact_dir, double fact_neu,
int num_front) const {
// Boundary condition for V^r //Construction of a Mtbl_cf from Valeur with Ylm coefficients
Valeur limit_vr (bound_vr) ;
limit_vr.coef() ;
limit_vr.ylm() ; // Spherical harmonics transform.
Mtbl_cf lim_vr (*(limit_vr.c_cf)) ;
// bound_vt and bound_vp are only known at the boundary --> we fill
// all the zones extending the values at the boundary before calling to poisson_angu.
Scalar temp_vt (*mp) ;
Scalar temp_vp (*mp) ;
temp_vt.annule_hard() ;
temp_vp.annule_hard() ;
int nz = mp->get_mg()->get_nzone() ;
for (int l=0; l<nz; l++)
for (int j=0; j<mp->get_mg()->get_nt(l); j++)
for (int k=0; k<mp->get_mg()->get_np(l); k++) {
temp_vt.set_grid_point(l, k, j, 0) = bound_vt(1, k, j, 0) ;
temp_vp.set_grid_point(l, k, j, 0) = bound_vp(1, k, j, 0) ;
}
temp_vt.set_spectral_va().set_base(bound_vt.base) ; // We set the basis
temp_vp.set_spectral_va().set_base(bound_vp.base) ;
cout << "temp_vp" << endl << norme(temp_vp) << endl ;
//Source for eta
Scalar source_eta(*mp) ;
Scalar vtstant (temp_vt) ;
vtstant.div_tant() ;
source_eta = temp_vt.dsdt() + vtstant + temp_vp.stdsdp() ;
//Source for mu
Scalar source_mu(*mp) ;
Scalar vpstant (temp_vp) ;
vpstant.div_tant() ;
source_mu = temp_vp.dsdt() + vpstant - temp_vt.stdsdp() ; //There was a wrong sign here
Scalar temp_mu (source_mu.poisson_angu()) ;
Scalar temp_eta (source_eta.poisson_angu()) ;
// Boundary condition for mu
Valeur limit_mu ((*mp).get_mg()->get_angu() ) ;
int nnp = (*mp).get_mg()->get_np(1) ;
int nnt = (*mp).get_mg()->get_nt(1) ;
limit_mu= 1 ;
for (int k=0 ; k<nnp ; k++)
for (int j=0 ; j<nnt ; j++)
limit_mu.set(1, k, j, 0) = temp_mu.val_grid_point(1, k, j, 0) ;
limit_mu.set_base(temp_mu.get_spectral_va().get_base()) ;
limit_mu.coef() ;
limit_mu.ylm() ; // Spherical harmonics transform.
Mtbl_cf lim_mu (*(limit_mu.c_cf)) ;
// Boundary condition for eta
Valeur limit_eta ((*mp).get_mg()->get_angu() ) ;
limit_eta = 1 ;
for (int k=0 ; k<nnp ; k++)
for (int j=0 ; j<nnt ; j++)
limit_eta.set(1, k, j, 0) = temp_eta.val_grid_point(1, k, j, 0) ;
limit_eta.set_base(temp_eta.get_spectral_va().get_base()) ;
limit_eta.coef() ;
limit_eta.ylm() ; // Spherical harmonics transform.
Mtbl_cf lim_eta (*(limit_eta.c_cf)) ;
// Call to poisson_boundary(...)
bool nullite = true ;
for (int i=0; i<3; i++) {
assert(cmp[i]->check_dzpuis(4)) ;
if (cmp[i]->get_etat() != ETATZERO || bound_vr.get_etat() != ETATZERO ||
bound_vt.get_etat() != ETATZERO || bound_vp.get_etat() != ETATZERO)
nullite = false ;
}
Vector resu(*mp, CON, triad) ;
if (nullite)
resu.set_etat_zero() ;
else
poisson_boundary(lam, lim_vr, lim_eta, lim_mu, num_front, fact_dir,
fact_neu, resu) ;
return resu ;
}
}
Lorene::Base_val
Bases of the spectral expansions.
Definition base_val.h:322
Lorene::Base_val::give_quant_numbers
void give_quant_numbers(int, int, int, int &, int &, int &) const
Computes the various quantum numbers and 1d radial base.
Definition base_val_quantum.C:81
Lorene::Base_vect_spher
Spherical orthonormal vectorial bases (triads).
Definition base_vect.h:308
Lorene::Diff_dsdx2
Class for the elementary differential operator (see the base class Diff ).
Definition diff.h:172
Lorene::Diff_dsdx2::get_matrice
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition diff_dsdx2.C:91
Lorene::Diff_dsdx
Class for the elementary differential operator (see the base class Diff ).
Definition diff.h:129
Lorene::Diff_dsdx::get_matrice
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition diff_dsdx.C:94
Lorene::Diff_id
Class for the elementary differential operator Identity (see the base class Diff ).
Definition diff.h:210
Lorene::Diff_x2dsdx2
Class for the elementary differential operator (see the base class Diff ).
Definition diff.h:490
Lorene::Diff_x2dsdx2::get_matrice
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition diff_x2dsdx2.C:95
Lorene::Diff_xdsdx2
Class for the elementary differential operator (see the base class Diff ).
Definition diff.h:531
Lorene::Diff_xdsdx2::get_matrice
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition diff_xdsdx2.C:97
Lorene::Diff_xdsdx
Class for the elementary differential operator (see the base class Diff ).
Definition diff.h:409
Lorene::Diff_xdsdx::get_matrice
virtual const Matrice & get_matrice() const
Returns the matrix associated with the operator.
Definition diff_xdsdx.C:98
Lorene::Map_af
Affine radial mapping.
Definition map.h:2027
Lorene::Map_af::get_beta
const double * get_beta() const
Returns the pointer on the array beta.
Definition map_af.C:481
Lorene::Map_af::get_alpha
const double * get_alpha() const
Returns the pointer on the array alpha.
Definition map_af.C:477
Lorene::Matrice
Matrix handling.
Definition matrice.h:152
Lorene::Matrice::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition matrice.C:175
Lorene::Matrice::set
double & set(int j, int i)
Read/write of a particuliar element.
Definition matrice.h:277
Lorene::Matrice::inverse
Tbl inverse(const Tbl &sec_membre) const
Solves the linear system represented by the matrix.
Definition matrice.C:424
Lorene::Matrice::set_band
void set_band(int up, int low) const
Calculate the band storage of *std.
Definition matrice.C:364
Lorene::Matrice::set_lu
void set_lu() const
Calculate the LU-representation, assuming the band-storage has been done.
Definition matrice.C:392
Lorene::Mg3d
Multi-domain grid.
Definition grilles.h:273
Lorene::Mg3d::get_angu
const Mg3d * get_angu() const
Returns the pointer on the associated angular grid.
Definition mg3d.C:473
Lorene::Mg3d::get_np
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition grilles.h:462
Lorene::Mg3d::get_nt
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition grilles.h:457
Lorene::Mg3d::get_nzone
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
Lorene::Mg3d::get_nr
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition grilles.h:452
Lorene::Mg3d::get_type_r
int get_type_r(int l) const
Returns the type of sampling in the radial direction in domain no.
Definition grilles.h:474
Lorene::Mtbl_cf
Coefficients storage for the multi-domain spectral method.
Definition mtbl_cf.h:186
Lorene::Mtbl_cf::set
Tbl & set(int l)
Read/write of the Tbl containing the coefficients in a given domain.
Definition mtbl_cf.h:294
Lorene::Mtbl_cf::annule_hard
void annule_hard()
Sets the Mtbl_cf to zero in a hard way.
Definition mtbl_cf.C:312
Lorene::Param_elliptic
This class contains the parameters needed to call the general elliptic solver.
Definition param_elliptic.h:135
Lorene::Param_elliptic::set_poisson_vect_r
void set_poisson_vect_r(int zone, bool only_l_zero=false)
Sets the operator to in all domains, for ; and to in all domains otherwise.
Definition param_elliptic.C:487
Lorene::Scalar::dsdt
const Scalar & dsdt() const
Returns of *this .
Definition scalar_deriv.C:208
Lorene::Scalar::set_etat_qcq
virtual void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition scalar.C:353
Lorene::Scalar::poisson_angu
Scalar poisson_angu(double lambda=0) const
Solves the (generalized) angular Poisson equation with *this as source.
Definition scalar_pde.C:200
Lorene::Scalar::val_grid_point
double val_grid_point(int l, int k, int j, int i) const
Returns the value of the field at a specified grid point.
Definition scalar.h:637
Lorene::Scalar::stdsdp
const Scalar & stdsdp() const
Returns of *this .
Definition scalar_deriv.C:238
Lorene::Scalar::div_tant
void div_tant()
Division by .
Definition scalar_th_manip.C:111
Lorene::Scalar::set_spectral_va
Valeur & set_spectral_va()
Returns va (read/write version).
Definition scalar.h:604
Lorene::Scalar::get_spectral_va
const Valeur & get_spectral_va() const
Returns va (read only version).
Definition scalar.h:601
Lorene::Scalar::annule_hard
void annule_hard()
Sets the Scalar to zero in a hard way.
Definition scalar.C:380
Lorene::Scalar::get_etat
int get_etat() const
Returns the logical state ETATNONDEF (undefined), ETATZERO (null) or ETATQCQ (ordinary).
Definition scalar.h:554
Lorene::Scalar::sol_elliptic_boundary
Scalar sol_elliptic_boundary(Param_elliptic &params, const Mtbl_cf &bound, double fact_dir, double fact_neu) const
Resolution of a general elliptic equation, putting zero at infinity and with inner boundary condition...
Definition scalar_pde.C:256
Lorene::Scalar::set_grid_point
double & set_grid_point(int l, int k, int j, int i)
Setting the value of the field at a given grid point.
Definition scalar.h:684
Lorene::Scalar::set_spectral_base
void set_spectral_base(const Base_val &)
Sets the spectral bases of the Valeur va.
Definition scalar.C:797
Lorene::Tbl
Basic array class.
Definition tbl.h:161
Lorene::Tbl::annule_hard
void annule_hard()
Sets the Tbl to zero in a hard way.
Definition tbl.C:372
Lorene::Tbl::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tbl.C:361
Lorene::Tbl::set
double & set(int i)
Read/write of a particular element (index i) (1D case).
Definition tbl.h:281
Lorene::Tbl::t
double * t
The array of double.
Definition tbl.h:173
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition valeur.h:287
Lorene::Valeur::set_etat_cf_qcq
void set_etat_cf_qcq()
Sets the logical state to ETATQCQ (ordinary state) for values in the configuration space (Mtbl_cf c_c...
Definition valeur.C:712
Lorene::Valeur::get_base
const Base_val & get_base() const
Return the bases for spectral expansions (member base ).
Definition valeur.h:480
Lorene::Valeur::get_etat
int get_etat() const
Returns the logical state.
Definition valeur.h:726
Lorene::Valeur::set_base
void set_base(const Base_val &)
Sets the bases for spectral expansions (member base ).
Definition valeur.C:810
Lorene::Valeur::ylm
void ylm()
Computes the coefficients of *this.
Definition valeur_ylm.C:138
Lorene::Valeur::set
Tbl & set(int l)
Read/write of the value in a given domain (configuration space).
Definition valeur.h:363
Lorene::Valeur::c_cf
Mtbl_cf * c_cf
Coefficients of the spectral expansion of the function.
Definition valeur.h:302
Lorene::Valeur::coef
void coef() const
Computes the coeffcients of *this.
Definition valeur_coef.C:148
Lorene::Valeur::ylm_i
void ylm_i()
Inverse of ylm().
Definition valeur_ylm_i.C:131
Lorene::Valeur::base
Base_val base
Bases on which the spectral expansion is performed.
Definition valeur.h:305
Lorene::Vector
Tensor field of valence 1.
Definition vector.h:188
Lorene::Vector::poisson_boundary
void poisson_boundary(double lambda, const Mtbl_cf &limit_vr, const Mtbl_cf &limit_eta, const Mtbl_cf &limit_mu, int num_front, double fact_dir, double fact_neu, Vector &resu) const
Solves the vector Poisson equation with *this as a source with a boundary condition on the excised sp...
Definition vector_poisson_boundary.C:65
Lorene::Vector::mu
virtual const Scalar & mu() const
Gives the field such that the angular components of the vector are written:
Definition vector_etamu.C:98
Lorene::Vector::poisson_neumann
Vector poisson_neumann(double lambda, const Valeur &limit_vr, const Valeur &limit_vt, const Valeur &limit_vp, int num_front) const
Solves the vector Poisson equation with *this as a source with a boundary condition on the excised sp...
Definition vector_poisson_boundary.C:691
Lorene::Vector::Vector
Vector(const Map &map, int tipe, const Base_vect &triad_i)
Standard constructor.
Definition vector.C:156
Lorene::Vector::eta
virtual const Scalar & eta() const
Gives the field such that the angular components of the vector are written:
Definition vector_etamu.C:66
Lorene::Vector::poisson_robin
Vector poisson_robin(double lambda, const Valeur &limit_vr, const Valeur &limit_vt, const Valeur &limit_vp, double fact_dir, double fact_neu, int num_front) const
Solves the vector Poisson equation with *this as a source with a boundary condition on the excised sp...
Definition vector_poisson_boundary.C:702
Lorene::Vector::set_vr_eta_mu
void set_vr_eta_mu(const Scalar &vr_i, const Scalar &eta_i, const Scalar &mu_i)
Defines the components through potentials and (see members p_eta and p_mu ), as well as the compon...
Definition vector_etamu.C:189
Lorene::norme
Tbl norme(const Cmp &)
Sums of the absolute values of all the values of the Cmp in each domain.
Definition cmp_math.C:481
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Lorene::Tensor::mp
const Map *const mp
Mapping on which the numerical values at the grid points are defined.
Definition tensor.h:295
Lorene::Tensor::cmp
Scalar ** cmp
Array of size n_comp of pointers onto the components.
Definition tensor.h:315
Lorene::Tensor::set_etat_zero
virtual void set_etat_zero()
Sets the logical state of all components to ETATZERO (zero state).
Definition tensor.C:497
Lorene::Tensor::triad
const Base_vect * triad
Vectorial basis (triad) with respect to which the tensor components are defined.
Definition tensor.h:303
Lorene
Lorene prototypes.
Definition app_hor.h:64