dirichlet_hdg_post_rt.cc

The Poisson problem by the hybrid discontinuous Galerkin method – post-treatment with the Raviart-Thomas element

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc, argv);
Float n, beta;
field sigma_h, uh, lambda_h;
din >> catchmark("n") >> n
>> catchmark("beta") >> beta
>> catchmark("u") >> uh
>> catchmark("lambda") >> lambda_h
>> catchmark("sigma") >> sigma_h;
const geo& omega = uh.get_geo();
size_t d = omega.dimension();
size_t k = uh.get_space().degree();
string approx = (k == 0) ? "empty" : "P"+itos(k-1)+"d";
space Tht(omega, "RT"+itos(k)+"d");
space Wht(omega, approx, "vector");
space Mht(omega, "trace(P"+itos(k)+"d)");
space Sht = Wht*Mht;
trial sigma_t (Tht); test tau (Sht);
auto tau_internal = tau[0], tau_n = tau[1];
auto coef = beta*pow(h_local(),n);
form aht = integrate (dot(sigma_t, tau_internal)
+ on_local_sides (dot(sigma_t,normal())*tau_n));
field lht = integrate(dot(sigma_h, tau_internal)
+ on_local_sides((dot(sigma_h,normal())
+ coef*(lambda_h - uh))*tau_n));
field sigma_ht (Tht);
problem p (aht);
p.solve (lht, sigma_ht);
dout << catchmark("n") << n << endl
<< catchmark("beta") << beta << endl
<< catchmark("u") << uh
<< catchmark("lambda") << lambda_h
<< catchmark("sigma") << sigma_h
<< catchmark("sigmat") << sigma_ht;
}
form
see the form page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
field
see the field page for the full documentation
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
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
rheolef::h_local
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
Definition: field_expr_terminal.h:527
space
see the space page for the full documentation
rheolef::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25
rheolef::on_local_sides
std::enable_if< details::is_field_expr_v2_variational_arg< Expr >::value,details::field_expr_quadrature_on_sides< Expr > >::type on_local_sides(const Expr &expr)
on_local_sides(expr): see the expression page for the full documentation
Definition: field_expr_quadrature.h:321
rheolef::din
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
test
see the test page for the full documentation
problem
see the problem page for the full documentation
Float
see the Float page for the full documentation
mkgeo_ball.d
d
Definition: mkgeo_ball.sh:154
mkgeo_ball.n
n
Definition: mkgeo_ball.sh:150
main
int main(int argc, char **argv)
Definition: dirichlet_hdg_post_rt.cc:28
trial
see the test page for the full documentation
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::itos
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef::std
Definition: vec_expr_v2.h:391
geo
see the geo page for the full documentation
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60