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dirichlet_hdg.cc
Go to the documentation of this file.
#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"] = lazy_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];
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition environment.h:121
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition integrate_option.h:125
rheolef::integrate_option::invert
bool invert
Definition integrate_option.h:168
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
main
int main()
Definition field2bb.cc:58
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
rheolef::div_h
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::divergence > >::type div_h(const Expr &expr)
div_h(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:1088
rheolef::lazy_interpolate
field_basic< T, M > lazy_interpolate(const space_basic< T, M > &X2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition field.h:871
rheolef::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition space_mult.h:120
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:432
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:211
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:323
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:520
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
Definition vec_expr_v2.h:415
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
std
STL namespace.
d
size_t d
Definition neumann-laplace-lambda.cc:28
rheolef.h
rheolef - reference manual
sinusprod_dirichlet.h
The sinus product function – right-hand-side and boundary condition for the Poisson problem.
f
Definition cavity_dg.h:29
g
Definition cavity_dg.h:25
lambda
Definition yield_slip_circle.h:34
p
Definition sphere.icc:25
sigma
Definition mosolov_exact_circle.h:40
u
Definition leveque.h:25