Rheolef  7.2
an efficient C++ finite element environment
dirichlet_hdg_post.cc

The Poisson problem by the hybrid discontinuous Galerkin method – post-treatment

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc, argv);
field uh, lambda_h, sigma_h;
din >> catchmark("n") >> n
>> catchmark("beta") >> beta
>> catchmark("u") >> uh
>> catchmark("lambda") >> lambda_h
>> catchmark("sigma") >> sigma_h;
field bar_uh = dirichlet_hdg_average (uh, lambda_h);
const geo& omega = uh.get_geo();
size_t d = omega.dimension();
size_t k = uh.get_space().degree();
space Xhs (omega, "P"+to_string(k+1)+"d"),
Zhs (omega, "P0"),
Yhs = Xhs*Zhs;
trial x(Yhs); test y(Yhs);
auto us = x[0], zeta = x[1];
auto vs = y[0], xi = y[1];
integrate_option iopt;
iopt.invert = true;
form inv_ahs = integrate(dot(grad_h(us),grad_h(vs)) + zeta*vs + xi*us, iopt);
field lhs = integrate (f(d)*vs + xi*bar_uh
+ on_local_sides(dot(sigma_h,normal())*vs));
field xhs = inv_ahs*lhs;
dout << catchmark("n") << n << endl
<< catchmark("beta") << beta << endl
<< catchmark("u") << xhs[0]
<< catchmark("lambda") << lambda_h
<< catchmark("sigma") << sigma_h
<< catchmark("zeta") << xhs[1];
}
see the Float page for the full documentation
see the field page for the full documentation
see the form page for the full documentation
see the geo page for the full documentation
idiststream din(cin)
see the diststream page for the full documentation
Definition: diststream.h:464
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:467
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
The Poisson problem by the hybrid discontinuous Galerkin method – local averaging function.
field dirichlet_hdg_average(field uh, field lambda_h)
int main(int argc, char **argv)
This file is part of Rheolef.
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
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
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:211
std::enable_if< details::has_field_rdof_interface< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Float beta[][pmax+1]
rheolef - reference manual
The sinus product function – right-hand-side and boundary condition for the Poisson problem.