laplace_band_error.cc
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#include "rheolef.h"
using namespace std;
using namespace rheolef;
#include "torus.icc"
int main (int argc, char**argv) {
environment rheolef (argc, argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-7;
bool do_dump = (argc > 2) ? true : false;
field phi_h;
din >> catchmark("phi") >> phi_h;
const space& Xh = phi_h.get_space();
band gamma_h (phi_h);
space Bh (gamma_h.band(), "P1");
field uh(Bh);
din >> catchmark("u") >> uh;
trial u (Bh); test v (Bh);
form m = integrate (gamma_h, u*v);
form a = integrate (gamma_h, dot(grad_s(u),grad_s(v)));
size_t d = Bh.get_geo().dimension();
field pi_h_u = interpolate(Bh, u_exact(d));
field eh = pi_h_u - uh;
field phi_h_band = phi_h [gamma_h.band()];
Float c1 = m(eh,phi_h_band)/m(phi_h_band,phi_h_band);
field one (Bh, 1);
Float meas_gamma = m(one,one);
Float c2 = m(one,eh)/meas_gamma;
eh = eh - c1*phi_h_band - c2*one;
Float err_l2 = sqrt(m(eh,eh));
Float err_h1 = sqrt(a(eh,eh));
derr << "err_l2 = " << err_l2 << endl
<< "err_h1 = " << err_h1 << endl;
if (do_dump) {
dout << catchmark ("u") << uh
<< catchmark ("ue") << pi_h_u
<< catchmark ("eh") << eh;
}
return (err_l2 < tol && err_h1 < tol) ? 0 : 1;
}
form
see the form page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
mkgeo_contraction.c2
c2
Definition: mkgeo_contraction.sh:199
field
see the field page for the full documentation
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
band
see the band page for the full documentation
space
see the space page for the full documentation
rheolef.h
rheolef - reference manual
main
int main(int argc, char **argv)
Definition: laplace_band_error.cc:25
a
Definition: diffusion_isotropic.h:25
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
eh
field_basic< T, M > eh
Definition: form_field_expr.h:58
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef::grad_s
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_s(const Expr &expr)
grad_s(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:929
mkgeo_sector.m
m
Definition: mkgeo_sector.sh:118
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
test
see the test page for the full documentation
u
Definition: leveque.h:25
rheolef::din
idiststream din(cin)
see the diststream page for the full documentation
u_exact
g u_exact
Definition: taylor_exact.h:26
Float
see the Float page for the full documentation
mkgeo_ball.d
d
Definition: mkgeo_ball.sh:154
u
Float u(const point &x)
Definition: transmission_error.cc:26
mkgeo_ball.a
a
Definition: mkgeo_ball.sh:151
trial
see the test page for the full documentation
torus.icc
The torus benchmark – level set, right-hand-side and exact solution.
rheolef::std
Definition: vec_expr_v2.h:391
rheolef::details::dot
rheolef::details::is_vec dot