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/*
* Solution of the l=0 part of the vector Poisson equation (only r-component)
*
*/
/*
* Copyright (c) 2007 Jerome Novak
*
* 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 pois_vect_r0_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/PDE/pois_vect_r0.C,v 1.2 2014/10/13 08:53:29 j_novak Exp $" ;
/*
* $Id: pois_vect_r0.C,v 1.2 2014/10/13 08:53:29 j_novak Exp $
* $Log: pois_vect_r0.C,v $
* Revision 1.2 2014/10/13 08:53:29 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.1 2007/01/23 17:08:46 j_novak
* New function pois_vect_r0.C to solve the l=0 part of the vector Poisson
* equation, which involves only the r-component.
*
*
* $Header: /cvsroot/Lorene/C++/Source/Non_class_members/PDE/pois_vect_r0.C,v 1.2 2014/10/13 08:53:29 j_novak Exp $
*
*/
// Lorene headers
#include "metric.h"
#include "proto.h"
#include "diff.h"
/*
* This function solves for the l=0 component of
*
* d2 f 2 df 2f
* ---- + - -- - -- = source
* dr2 r dr r2
*
* and returns the soluton f.
* The input Scalar must have dzpuis = 4.
*/
namespace Lorene {
Scalar pois_vect_r0(const Scalar& source) {
const Map& map0 = source.get_mp() ;
const Map_af* map1 = dynamic_cast<const Map_af*>(&map0) ;
assert(map1 != 0x0) ;
const Map_af& map = *map1 ;
const Mg3d& mgrid = *map.get_mg() ;
int nz = mgrid.get_nzone() ;
Scalar resu(map) ;
if (source.get_etat() == ETATZERO) {
resu = 0 ;
return resu ;
}
resu.annule_hard() ;
resu.std_spectral_base_odd() ;
resu.set_spectral_va().ylm() ;
Mtbl_cf& sol_coef = (*resu.set_spectral_va().c_cf) ;
const Base_val& base = source.get_spectral_base() ;
assert(resu.get_spectral_base() == base) ;
assert(source.check_dzpuis(4)) ;
Mtbl_cf sol_part(mgrid, base) ; sol_part.annule_hard() ;
Mtbl_cf sol_hom1(mgrid, base) ; sol_hom1.annule_hard() ;
Mtbl_cf sol_hom2(mgrid, base) ; sol_hom2.annule_hard() ;
{ int lz = 0 ;
int nr = mgrid.get_nr(lz) ;
double alpha2 = map.get_alpha()[lz]*map.get_alpha()[lz] ;
assert(mgrid.get_type_r(lz) == RARE) ;
int base_r = R_CHEBI ;
Matrice ope(nr,nr) ;
ope.annule_hard() ;
Diff_dsdx2 dx2(base_r, nr) ; const Matrice& mdx2 = dx2.get_matrice() ;
Diff_sxdsdx sdx(base_r, nr) ; const Matrice& msdx = sdx.get_matrice() ;
Diff_sx2 sx2(base_r, nr) ; const Matrice& ms2 = sx2.get_matrice() ;
for (int lin=0; lin<nr-1; lin++)
for (int col=0; col<nr; col++)
ope.set(lin,col) = (mdx2(lin,col) + 2*msdx(lin,col) - 2*ms2(lin,col))/alpha2 ;
ope.set(nr-1, 0) = 1 ; //for the true homogeneous solution
for (int i=1; i<nr; i++)
ope.set(nr-1, i) = 0 ;
Tbl rhs(nr) ;
rhs.annule_hard() ;
for (int i=0; i<nr-1; i++)
rhs.set(i) = (*source.get_spectral_va().c_cf)(lz, 0, 0, i) ;
rhs.set(nr-1) = 0 ;
ope.set_lu() ;
Tbl sol = ope.inverse(rhs) ;
for (int i=0; i<nr; i++)
sol_part.set(lz, 0, 0, i) = sol(i) ;
rhs.annule_hard() ;
rhs.set(nr-1) = 1 ;
sol = ope.inverse(rhs) ;
for (int i=0; i<nr; i++)
sol_hom1.set(lz, 0, 0, i) = sol(i) ;
}
for (int lz=1; lz<nz-1; lz++) {
int nr = mgrid.get_nr(lz) ;
double alpha = map.get_alpha()[lz] ;
double beta = map.get_beta()[lz] ;
double ech = beta / alpha ;
assert(mgrid.get_type_r(lz) == FIN) ;
int base_r = R_CHEB ;
Matrice ope(nr,nr) ;
ope.annule_hard() ;
Diff_dsdx dx(base_r, nr) ; const Matrice& mdx = dx.get_matrice() ;
Diff_dsdx2 dx2(base_r, nr) ; const Matrice& mdx2 = dx2.get_matrice() ;
Diff_id id(base_r, nr) ; const Matrice& mid = id.get_matrice() ;
Diff_xdsdx xdx(base_r, nr) ; const Matrice& mxdx = xdx.get_matrice() ;
Diff_xdsdx2 xdx2(base_r, nr) ; const Matrice& mxdx2 = xdx2.get_matrice() ;
Diff_x2dsdx2 x2dx2(base_r, nr) ; const Matrice& mx2dx2 = x2dx2.get_matrice() ;
for (int lin=0; lin<nr-2; lin++)
for (int col=0; col<nr; col++)
ope.set(lin, col) = mx2dx2(lin, col) + 2*ech*mxdx2(lin, col) + ech*ech*mdx2(lin, col)
+ 2*(mxdx(lin, col) + ech*mdx(lin, col)) - 2*mid(lin, col) ;
ope.set(nr-2, 0) = 0 ;
ope.set(nr-2, 1) = 1 ;
for (int col=2; col<nr; col++) {
ope.set(nr-2, col) = 0 ;
}
ope.set(nr-1, 0) = 1 ;
for (int col=1; col<nr; col++)
ope.set(nr-1, col) = 0 ;
Tbl src(nr) ;
src.set_etat_qcq() ;
for (int i=0; i<nr; i++)
src.set(i) = (*source.get_spectral_va().c_cf)(lz, 0, 0, i) ;
Tbl xsrc = src ; multx_1d(nr, &xsrc.t, base_r) ;
Tbl x2src = src ; multx2_1d(nr, &x2src.t, base_r) ;
Tbl rhs(nr) ;
rhs.set_etat_qcq() ;
for (int i=0; i<nr-2; i++)
rhs.set(i) = beta*beta*src(i) + 2*beta*alpha*xsrc(i) + alpha*alpha*x2src(i) ;
rhs.set(nr-2) = 0 ;
rhs.set(nr-1) = 0 ;
ope.set_lu() ;
Tbl sol = ope.inverse(rhs) ;
for (int i=0; i<nr; i++)
sol_part.set(lz, 0, 0, i) = sol(i) ;
rhs.annule_hard() ;
rhs.set(nr-2) = 1 ;
sol = ope.inverse(rhs) ;
for (int i=0; i<nr; i++)
sol_hom1.set(lz, 0, 0, i) = sol(i) ;
rhs.set(nr-2) = 0 ;
rhs.set(nr-1) = 1 ;
sol = ope.inverse(rhs) ;
for (int i=0; i<nr; i++)
sol_hom2.set(lz, 0, 0, i) = sol(i) ;
}
{ int lz = nz-1 ;
int nr = mgrid.get_nr(lz) ;
double alpha2 = map.get_alpha()[lz]*map.get_alpha()[lz] ;
assert(mgrid.get_type_r(lz) == UNSURR) ;
int base_r = R_CHEBU ;
Matrice ope(nr,nr) ;
ope.annule_hard() ;
Diff_dsdx2 dx2(base_r, nr) ; const Matrice& mdx2 = dx2.get_matrice() ;
Diff_sx2 sx2(base_r, nr) ; const Matrice& ms2 = sx2.get_matrice() ;
for (int lin=0; lin<nr-3; lin++)
for (int col=0; col<nr; col++)
ope.set(lin, col) = (mdx2(lin, col) - 2*ms2(lin, col))/alpha2 ;
for (int i=0; i<nr; i++) {
ope.set(nr-3, i) = i*i ; //for the finite part (derivative = 0 at infty)
}
for (int i=0; i<nr; i++) {
ope.set(nr-2, i) = 1 ; //for the limit at inifinity
}
ope.set(nr-1, 0) = 1 ; //for the true homogeneous solution
for (int i=1; i<nr; i++)
ope.set(nr-1, i) = 0 ;
Tbl rhs(nr) ;
rhs.annule_hard() ;
for (int i=0; i<nr-3; i++)
rhs.set(i) = (*source.get_spectral_va().c_cf)(lz, 0, 0, i) ;
rhs.set(nr-3) = 0 ;
rhs.set(nr-2) = 0 ;
rhs.set(nr-1) = 0 ;
ope.set_lu() ;
Tbl sol = ope.inverse(rhs) ;
for (int i=0; i<nr; i++)
sol_part.set(lz, 0, 0, i) = sol(i) ;
rhs.annule_hard() ;
rhs.set(nr-1) = 1 ;
sol = ope.inverse(rhs) ;
for (int i=0; i<nr; i++)
sol_hom2.set(lz, 0, 0, i) = sol(i) ;
}
Mtbl_cf dpart = sol_part ; dpart.dsdx() ;
Mtbl_cf dhom1 = sol_hom1 ; dhom1.dsdx() ;
Mtbl_cf dhom2 = sol_hom2 ; dhom2.dsdx() ;
Matrice systeme(2*(nz-1), 2*(nz-1)) ;
systeme.annule_hard() ;
Tbl rhs(2*(nz-1)) ;
rhs.annule_hard() ;
//Nucleus
int lin = 0 ;
int col = 0 ;
double alpha = map.get_alpha()[0] ;
systeme.set(lin,col) = sol_hom1.val_out_bound_jk(0, 0, 0) ;
rhs.set(lin) -= sol_part.val_out_bound_jk(0, 0, 0) ;
lin++ ;
systeme.set(lin,col) = dhom1.val_out_bound_jk(0, 0, 0) / alpha ;
rhs.set(lin) -= dpart.val_out_bound_jk(0, 0, 0) / alpha ;
col++ ;
//Shells
for (int lz=1; lz<nz-1; lz++) {
alpha = map.get_alpha()[lz] ;
lin-- ;
systeme.set(lin,col) -= sol_hom1.val_in_bound_jk(lz, 0, 0) ;
systeme.set(lin,col+1) -= sol_hom2.val_in_bound_jk(lz, 0, 0) ;
rhs.set(lin) += sol_part.val_in_bound_jk(lz, 0, 0) ;
lin++ ;
systeme.set(lin,col) -= dhom1.val_in_bound_jk(lz, 0, 0) / alpha ;
systeme.set(lin,col+1) -= dhom2.val_in_bound_jk(lz, 0, 0) / alpha ;
rhs.set(lin) += dpart.val_in_bound_jk(lz, 0, 0) / alpha;
lin++ ;
systeme.set(lin, col) += sol_hom1.val_out_bound_jk(lz, 0, 0) ;
systeme.set(lin, col+1) += sol_hom2.val_out_bound_jk(lz, 0, 0) ;
rhs.set(lin) -= sol_part.val_out_bound_jk(lz, 0, 0) ;
lin++ ;
systeme.set(lin, col) += dhom1.val_out_bound_jk(lz, 0, 0) / alpha ;
systeme.set(lin, col+1) += dhom2.val_out_bound_jk(lz, 0, 0) / alpha ;
rhs.set(lin) -= dpart.val_out_bound_jk(lz, 0, 0) / alpha ;
col += 2 ;
}
//CED
alpha = map.get_alpha()[nz-1] ;
lin-- ;
systeme.set(lin,col) -= sol_hom2.val_in_bound_jk(nz-1, 0, 0) ;
rhs.set(lin) += sol_part.val_in_bound_jk(nz-1, 0, 0) ;
lin++ ;
systeme.set(lin,col) -= (-4*alpha)*dhom2.val_in_bound_jk(nz-1, 0, 0) ;
rhs.set(lin) += (-4*alpha)*dpart.val_in_bound_jk(nz-1, 0, 0) ;
systeme.set_lu() ;
Tbl coef = systeme.inverse(rhs) ;
int indice = 0 ;
for (int i=0; i<mgrid.get_nr(0); i++)
sol_coef.set(0, 0, 0, i) = sol_part(0, 0, 0, i)
+ coef(indice)*sol_hom1(0, 0, 0, i) ;
indice++ ;
for (int lz=1; lz<nz-1; lz++) {
for (int i=0; i<mgrid.get_nr(lz); i++)
sol_coef.set(lz, 0, 0, i) = sol_part(lz, 0, 0, i)
+coef(indice)*sol_hom1(lz, 0, 0, i)
+coef(indice+1)*sol_hom2(lz, 0, 0, i) ;
indice += 2 ;
}
for (int i=0; i<mgrid.get_nr(nz-1); i++)
sol_coef.set(nz-1, 0, 0, i) = sol_part(nz-1, 0, 0, i)
+coef(indice)*sol_hom2(nz-1, 0, 0, i) ;
delete resu.set_spectral_va().c ;
resu.set_spectral_va().c = 0x0 ;
resu.set_dzpuis(0) ;
resu.set_spectral_va().ylm_i() ;
return resu ;
}
}
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