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

Convection-diffusion equation by the hybrid discontinuous Galerkin method.

Convection-diffusion equation by the hybrid 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]);
string approx = (argc > 2) ? argv[2] : "P1d";
Float nu = (argc > 3) ? atof(argv[3]) : 1e-2;
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();
trial x(Yh);
test y(Yh);
test mu(Mh);
iopt.invert = true;
form inv_a = integrate((1/nu)*dot(x[0],y[0]) + x[1]*div_h(y[0])
+ y[1]*div_h(x[0]) - phi::sigma(d,nu)*x[1]*y[1]
+ x[1]*dot(u(d),grad_h(y[1]))
- on_local_sides((beta+abs(dot(u(d),normal())))*x[1]*y[1]), iopt);
form b1 = integrate("internal_sides", (-dot(jump(x[0]),normal())
+ 2*(beta+abs(dot(u(d),normal())))*average(x[1])
- dot(u(d),normal())*jump(x[1]))*mu);
form b2 = integrate("internal_sides", (-dot(jump(x[0]),normal())
+ 2*(beta+abs(dot(u(d),normal())))*average(x[1]))*mu);
form c = integrate("internal_sides",
2*(beta+abs(dot(u(d),normal())))*lambda*mu);
field lh = integrate(omega, -f(d,nu)*y[1])
+ integrate("boundary", phi(d,nu)*(dot(y[0],normal())
- (beta+abs(dot(u(d),normal()))-dot(u(d),normal()))*y[1]));
field kh(Mh,0), lambda_h(Mh,0);
lambda_h["boundary"] = lazy_interpolate(Wh,phi(d,nu));
form s = c + b2*inv_a*trans(b1);
field rh = b2*(inv_a*lh) - kh;
problem p(s);
p.solve (rh, lambda_h);
field xh = inv_a*(lh - b1.trans_mult(lambda_h));
dout << catchmark("nu") << nu << endl
<< catchmark("phi") << xh[1]
<< catchmark("sigma") << xh[0]
<< catchmark("lambda") << lambda_h;
}
field lh(Float epsilon, Float t, const test &v)
Float phi(const point &nu, Float a, Float b)
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 catchmark page for the full documentation
Definition: catchmark.h:67
see the environment page for the full documentation
Definition: environment.h:121
see the integrate_option page for the full documentation
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
int main(int argc, char **argv)
Definition: convect_hdg.cc:29
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::divergence > >::type div_h(const Expr &expr)
div_h(uh): see the expression page for the full documentation
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
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
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
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
Float beta[][pmax+1]
STL namespace.
rheolef - reference manual
Definition: nu.h:26
Definition: sphere.icc:25
Float sigma