Rheolef  7.2
an efficient C++ finite element environment
reconstruction_hho.cc
Go to the documentation of this file.
1
25#include "rheolef.h"
26using namespace rheolef;
27using namespace std;
28#include "sinusprod.h"
29#include "diffusion_isotropic.h"
30int main(int argc, char**argv) {
31 environment rheolef (argc, argv);
32 geo omega (argv[1]);
33 string Pkd = (argc > 2) ? argv[2] : "P0",
34 Pld = (argc > 3) ? argv[3] : Pkd;
35 space Xh (omega, Pld),
36 Mh (omega["sides"], Pkd);
37 size_t l = Xh.degree(), k = Xh.degree(), d = omega.dimension();
38 check_macro(l == k-1 || l == k || l == k+1,
39 "invalid (k,l) = ("<<k<<","<<l<<")");
40 space Xhs(omega, "P"+to_string(k+1)+"d"),
41 Zh (omega, "P0");
42 trial u(Xh), lambda(Mh), us(Xhs), zeta (Zh);
43 test v(Xh), mu (Mh), vs(Xhs), xi (Zh);
44 auto as = lazy_integrate (dot(grad_h(us),A(d)*grad_h(vs)));
45 auto bs = lazy_integrate (us*xi);
46 auto cs = lazy_integrate (pow(h_local(),2)*zeta*xi);
47 auto m = lazy_integrate (u*v);
49 auto inv_cs = inv(cs);
50 auto inv_m = inv(m);
51 auto inv_S = inv(as + trans(bs)*inv_cs*bs);
52 auto llh = lazy_integrate (u_exact(d)*v);
54 field pi_Xh_u = inv_m*llh;
55 field pi_Mh_lambda(Mh);
56 problem pms (ms);
57 pms.solve (rhs, pi_Mh_lambda);
58 field lh = lazy_integrate (dot(grad_h(pi_Xh_u),A(d)*grad_h(vs))
59 + on_local_sides((pi_Mh_lambda-pi_Xh_u)
60 *dot(normal(),A(d)*grad_h(vs))));
61 auto kh = lazy_integrate (pi_Xh_u*xi);
62 auto rh = lh + bs.trans_mult(inv_cs*kh);
63 field us_h = inv_S*rh;
64 field zeta_h = inv_cs*(bs*us_h - kh);
65 dout << catchmark("us") << us_h
66 << catchmark("zeta") << zeta_h;
67}
field lh(Float epsilon, Float t, const test &v)
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 space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
Tensor diffusion – isotropic case.
point u(const point &x)
check_macro(expr1.have_homogeneous_space(Xh1), "dual(expr1,expr2); expr1 should have homogeneous space. HINT: use dual(interpolate(Xh, expr1),expr2)")
rheolef::details::is_vec dot
This file is part of Rheolef.
tensor_basic< T > inv(const tensor_basic< T > &a, size_t d)
Definition: tensor.cc:219
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
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_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_quadrature_arg< Expr >::value, details::field_lazy_terminal_integrate< Expr > >::type lazy_integrate(const typename Expr::geo_type &domain, const Expr &expr, const integrate_option &iopt=integrate_option())
see the integrate page for the full documentation
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
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
STL namespace.
int main(int argc, char **argv)
rheolef - reference manual
The sinus product function.
Definition: leveque.h:25
g u_exact
Definition: taylor_exact.h:26