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

The Helmholtz problem with Neumann boundary conditions by the discontinuous Galerkin method.

The Helmholtz problem with Neumann boundary conditions by the discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
size_t d = omega.dimension();
size_t k = Xh.degree();
Float beta = (k+1)*(k+d)/Float(d);
trial u (Xh); test v (Xh);
form a = integrate (u*v + dot(grad_h(u),grad_h(v)))
+ integrate ("internal_sides",
beta*penalty()*jump(u)*jump(v)
- jump(u)*average(dot(grad_h(v),normal()))
- jump(v)*average(dot(grad_h(u),normal())));
field lh = integrate (f(d)*v) + integrate ("boundary", g(d)*v);
field uh(Xh);
problem p (a);
p.solve (lh, uh);
dout << uh;
}
u_exact g
field lh(Float epsilon, Float t, const test &v)
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
see the problem page for the full documentation
see the environment page for the full documentation
Definition: environment.h:121
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
point u(const point &x)
rheolef::details::is_vec dot
This file is part of Rheolef.
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::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
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
details::field_expr_v2_nonlinear_terminal_function< details::penalty_pseudo_function< Float > > penalty()
penalty(): see the expression page for the full documentation
Float beta[][pmax+1]
STL namespace.
int main(int argc, char **argv)
Definition: neumann_dg.cc:29
rheolef - reference manual
The sinus product function – right-hand-side and boundary condition for the Helmholtz problem.
Definition: sphere.icc:25
Definition: leveque.h:25