Rheolef  7.1
an efficient C++ finite element environment
helmholtz_s_error.cc

The Helmholtz problem on a surface – error analysis

#include "rheolef.h"
using namespace std;
using namespace rheolef;
#include "sphere.icc"
int main (int argc, char**argv) {
environment rheolef(argc, argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e+38;
field uh; din >> uh;
const space& Wh = uh.get_space();
trial u (Wh); test v (Wh);
form m = integrate (u*v);
size_t d = Wh.get_geo().dimension();
field pi_h_u = interpolate(Wh, u_exact(d));
field eh = uh - pi_h_u;
dout << "err_l2 " << sqrt(m(eh,eh)) << endl
<< "err_h1 " << sqrt(a(eh,eh)) << endl
<< "err_linf " << eh.max_abs() << endl;
return (eh.max_abs() < tol) ? 0 : 1;
}
form
see the form page for the full documentation
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
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
space
see the space page for the full documentation
rheolef.h
rheolef - reference manual
sphere.icc
The level set function for the sphere geometry.
main
int main(int argc, char **argv)
Definition: helmholtz_s_error.cc:29
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
u
Float u(const point &x)
Definition: transmission_error.cc:26
trial
see the test page for the full documentation
mkgeo_ball.a
int a
Definition: mkgeo_ball.sh:151
rheolef::details::dot
rheolef::details::is_vec dot