dirichlet_hdg.cc

The Poisson problem by the hybrid discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "sinusprod_dirichlet.h"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
string approx = (argc > 2) ? argv[2] : "P1d";
Float n = (argc > 3) ? atof(argv[3]) : 1;
Float beta = (argc > 4) ? atof(argv[4]) : 1;
space Th (omega, approx, "vector"),
Xh (omega, approx),
Yh = Th*Xh,
Mh (omega["sides"], approx);
Mh.block("boundary");
space Wh(Mh.get_geo()["boundary"],approx);
size_t d = omega.dimension();
size_t k = Xh.degree();
trial x(Yh), lambda(Mh);
test y(Yh), mu(Mh);
auto sigma = x[0], u = x[1];
auto tau = y[0], v = y[1];
integrate_option iopt;
iopt.invert = true;
auto coef = beta*pow(h_local(),n);
form inv_a = integrate(dot(sigma,tau) + u*div_h(tau) + v*div_h(sigma)
- on_local_sides(coef*u*v), iopt);
form b = integrate("internal_sides",
(-dot(jump(sigma),normal()) + 2*coef*average(u))*mu)
+ integrate("boundary", (-dot(sigma,normal()) + coef*u)*mu);
form c = integrate("internal_sides", 2*coef*lambda*mu)
+ integrate("boundary", coef*lambda*mu);
field lh = integrate (-f(d)*v);
field kh(Mh,0), lambda_h(Mh,0);
lambda_h ["boundary"] = interpolate (Wh, g(d));
form s = c + b*inv_a*trans(b);
field rh = b*(inv_a*lh) - kh;
problem p (s);
p.solve (rh, lambda_h);
field xh = inv_a*(lh - b.trans_mult(lambda_h));
dout << catchmark("n") << n << endl
<< catchmark("beta") << beta << endl
<< catchmark("u") << xh[1]
<< catchmark("lambda") << lambda_h
<< catchmark("sigma") << xh[0];
}
g
u_exact g
Definition: burgers_diffusion_exact.h:33
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
mkgeo_ball.f
f
Definition: mkgeo_ball.sh:221
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
mkgeo_ball.c
c
Definition: mkgeo_ball.sh:153
sinusprod_dirichlet.h
The sinus product function – right-hand-side and boundary condition for the Poisson problem.
rheolef::div_h
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::divergence >>::type div_h(const Expr &expr)
div_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:1069
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition: integrate_option.h:125
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::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
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
main
int main(int argc, char **argv)
Definition: dirichlet_hdg.cc:29
sigma
Definition: mosolov_exact_circle.h:40
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::integrate_option::invert
bool invert
Definition: integrate_option.h:168
test
see the test page for the full documentation
problem
see the problem page for the full documentation
u
Definition: leveque.h:25
Float
see the Float page for the full documentation
mkgeo_ball.d
d
Definition: mkgeo_ball.sh:154
mkgeo_ball.b
b
Definition: mkgeo_ball.sh:152
mkgeo_contraction.mu
mu
Definition: mkgeo_contraction.sh:193
mkgeo_ball.n
n
Definition: mkgeo_ball.sh:150
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::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
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
lambda
Definition: yield_slip_circle.h:34