Rheolef  7.1
an efficient C++ finite element environment
dirichlet_hdg.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "sinusprod_dirichlet.h"
29 int main(int argc, char**argv) {
30  environment rheolef (argc, argv);
31  geo omega (argv[1]);
32  string approx = (argc > 2) ? argv[2] : "P1d";
33  Float n = (argc > 3) ? atof(argv[3]) : 1;
34  Float beta = (argc > 4) ? atof(argv[4]) : 1;
35  space Th (omega, approx, "vector"),
36  Xh (omega, approx),
37  Yh = Th*Xh,
38  Mh (omega["sides"], approx);
39  Mh.block("boundary");
40  space Wh(Mh.get_geo()["boundary"],approx);
41  size_t d = omega.dimension();
42  size_t k = Xh.degree();
43  trial x(Yh), lambda(Mh);
44  test y(Yh), mu(Mh);
45  auto sigma = x[0], u = x[1];
46  auto tau = y[0], v = y[1];
47  integrate_option iopt;
48  iopt.invert = true;
49  auto coef = beta*pow(h_local(),n);
50  form inv_a = integrate(dot(sigma,tau) + u*div_h(tau) + v*div_h(sigma)
51  - on_local_sides(coef*u*v), iopt);
52  form b = integrate("internal_sides",
53  (-dot(jump(sigma),normal()) + 2*coef*average(u))*mu)
54  + integrate("boundary", (-dot(sigma,normal()) + coef*u)*mu);
55  form c = integrate("internal_sides", 2*coef*lambda*mu)
56  + integrate("boundary", coef*lambda*mu);
57  field lh = integrate (-f(d)*v);
58  field kh(Mh,0), lambda_h(Mh,0);
59  lambda_h ["boundary"] = interpolate (Wh, g(d));
60  form s = c + b*inv_a*trans(b);
61  field rh = b*(inv_a*lh) - kh;
62  problem p (s);
63  p.solve (rh, lambda_h);
64  field xh = inv_a*(lh - b.trans_mult(lambda_h));
65  dout << catchmark("n") << n << endl
66  << catchmark("beta") << beta << endl
67  << catchmark("u") << xh[1]
68  << catchmark("lambda") << lambda_h
69  << catchmark("sigma") << xh[0];
70 }
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 catchmark page for the full documentation
Definition: catchmark.h:67
see the environment page for the full documentation
Definition: environment.h:104
see the integrate_option page for the full documentation
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
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)
This file is part of Rheolef.
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
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
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 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:202
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
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
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.
Definition: sphere.icc:25
Definition: leveque.h:25