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// Lorene headers
#include "metric.h"
#include "cmp.h"
#include "nbr_spx.h"
#include "utilitaires.h"
#include "graphique.h"
using namespace Lorene ;
int main() {
// Construction of a multi-grid (Mg3d)
// -----------------------------------
const int nz = 3 ; // Number of domains
int nr =33 ; // Number of collocation points in r in each domain
int nt = 5 ; // Number of collocation points in theta in each domain
int np = 6 ; // Number of collocation points in phi in each domain
int symmetry_theta = SYM ; // symmetry with respect to the equatorial plane
int symmetry_phi = NONSYM ; // no symmetry in phi
int nbr[] = {nr, nr , nr};
int nbt[] = {nt, nt, nt} ;
int nbp[] = {np, np, np} ;
int tipe_r[] = {RARE, FIN, UNSURR} ;
assert( nz == 3 ) ;// since the above arrays are described in only 3 domains
int nzm1 = nz - 1 ;
Mg3d mgrid(nz, nbr, tipe_r, nbt, symmetry_theta, nbp, symmetry_phi) ;
// Construction of an affine mapping (Map_af)
// ------------------------------------------
// Boundaries of each domains
double r_limits[] = {0., 1., 2., __infinity} ;
Map_af map(mgrid, r_limits) ;
// Construction of flat metrics
// ----------------------------
Metric_flat mets(map, map.get_bvect_spher()) ; // spherical representation
Metric_flat metc(map, map.get_bvect_cart()) ; // Cartesian representation
// Construction of a divergence free vector field
// ----------------------------------------------
const Coord& r = map.r ;
Scalar sint(map), cost(map) ;
sint = map.sint ;
cost = map.cost ;
Scalar comp_l2 = 3*cost*cost - 1 ;
comp_l2.std_spectral_base() ;
Scalar num(map) ;
num = 3 - r*r*r*r ;
num.std_spectral_base() ;
Base_val ma_base(nz) ;
ma_base.set_base_r(0, R_CHEBPIM_I) ;
for (int i=1; i<nz-1; i++)
ma_base.set_base_r(i, R_CHEB) ;
ma_base.set_base_r(nz-1, R_CHEBU) ;
ma_base.set_base_t(T_COSSIN_CP) ;
ma_base.set_base_p(P_COSSIN) ;
Mtbl denom0(mgrid) ;
denom0 = 1/(r*r*r*r) ;
Scalar unsur4(map) ;
unsur4 = 1 / (1 + r*r*r*r) ;
unsur4.annule_domain(nz-1) ;
unsur4.std_spectral_base() ;
Scalar la_zec(map) ;
la_zec = 1 ;
la_zec.annule(0,nz-2) ;
la_zec.set_dzpuis(4) ;
Scalar tmp(map) ;
tmp = 1 / (1 + denom0) ;
tmp.annule(0, nz-2) ;
la_zec *= tmp ;
unsur4 += la_zec ;
Scalar rtrois(map), denom1(map), denom2(map), denom3(map) ;
rtrois = r*r*r ;
rtrois.set_spectral_base(ma_base) ;
denom1 = 1 / (r*r*r*r + 1) ;
denom1.std_spectral_base() ;
denom2 = unsur4 * denom1 ;
denom3 = denom2*denom1 ;
Scalar denom4 = denom3*denom1 ;
Vector vvs1(map, CON, map.get_bvect_spher()) ;
vvs1.set(1) = denom1 *comp_l2 ;
vvs1.set(1).set_outer_boundary(nzm1, 0) ;
vvs1.set(1).mult_r() ;
vvs1.set(1).set_outer_boundary(nzm1, 0) ;
vvs1.set(2) = - num*denom1*denom1 ;
vvs1.set(2).set_outer_boundary(nzm1, 0) ;
vvs1.set(2).mult_rsint() ;
vvs1.set(2).mult_cost() ;
vvs1.set(3) = -denom1 ;
vvs1.set(3).set_outer_boundary(nzm1, 0) ;
vvs1.set(3).mult_rsint() ;
vvs1.set(3).set_outer_boundary(nzm1, 0) ;
vvs1.std_spectral_base() ;
Vector source_s(map, CON, map.get_bvect_spher()) ;
source_s.set(1) = -(32 * denom3 + 4 * denom2)*rtrois*comp_l2 ;
source_s.set(1).set_outer_boundary(nzm1, 0) ;
source_s.set(2) = ( 384 * denom4 - 192 * denom3 - 12 * denom2)*rtrois ;
source_s.set(2).set_outer_boundary(nzm1, 0) ;
source_s.set(2).set_spectral_base(ma_base) ;
source_s.set(2).mult_sint() ;
source_s.set(2).mult_cost() ;
source_s.set(3) = (32*denom3 - 4 * denom2) * rtrois ;
source_s.set(3).set_outer_boundary(nzm1, 0) ;
source_s.std_spectral_base() ;
source_s.set(3).set_spectral_base(ma_base) ;
source_s.set(3).mult_sint() ;
cout << "Divergence of source : " << endl ;
cout << "---------------------- " << endl << endl ;
source_s.divergence(mets).spectral_display(0x0, 1.e-12) ;
int sd ; cin >> sd ;
Scalar pot_source = source_s.potential(mets) ;
cout << "Source potential: " << endl ;
cout << "----------------- " << endl << endl ;
pot_source.spectral_display(0x0, 1.e-13) ;
cin >> sd ;
Vector_divfree source_df = source_s.div_free(mets) ;
cout << "Difference with the div_free part of the source : " << endl;
cout << "------------------------------------------------- " << endl << endl ;
Vector v_diff = source_df - source_s ;
v_diff.dec_dzpuis(4) ;
v_diff.spectral_display(0x0, 1.e-13) ;
cout << endl ;
cin >> sd ;
Vector_divfree sol_df = source_df.poisson() ;
Vector diff_df = sol_df - vvs1 ;
cout << "Difference with analytic solution: " << endl ;
cout << "---------------------------------- " << endl ;
for (int i=1; i<4; i++)
cout << max(abs(diff_df(i))) << endl ;
cout << endl ;
Vector sol = sol_df ;
cout << "Divergence of the solution : " << endl ;
cout << "---------------------------- " << endl ;
Scalar dive = sol.divergence(mets) ;
dive.dec_dzpuis(2) ;
dive.spectral_display(0x0, 1.e-12) ;
Scalar eta_theo = num*denom1*denom1*comp_l2 / 6 ;
eta_theo.std_spectral_base() ;
eta_theo.set_outer_boundary(nzm1,0) ;
eta_theo.mult_r() ;
Scalar eta = sol_df.eta() ;
cout << "Difference in eta : " << endl ;
cout << "------------------- " << endl ;
cout << max(abs(eta- eta_theo)) << endl ;
Scalar mu_theo(map) ;
mu_theo = denom1 ;
mu_theo.set_outer_boundary(nzm1,0) ;
mu_theo.mult_r() ;
mu_theo.mult_cost() ;
Scalar mu = sol_df.mu() ;
cout << "Diffrence in mu: " << endl ;
cout << "------------------- " << endl ;
cout << max(abs(mu - mu_theo)) << endl ;
return EXIT_SUCCESS ;
}
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