Rheolef  7.2
an efficient C++ finite element environment
 
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dirichlet_hho.cc
Go to the documentation of this file.
1
25#include "rheolef.h"
26using namespace rheolef;
27using namespace std;
28#include "sinusprod_dirichlet.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] : "P1d",
34 Pld = (argc > 3) ? argv[3] : Pkd;
35 space Xh (omega, Pld),
36 Mh (omega["sides"], Pkd);
37 Mh.block("boundary");
38 size_t k = Mh.degree(), l = Xh.degree(), dim = omega.dimension();
39 Float beta = (argc > 4) ? atof(argv[4]) : 10*(k+1)*(k+dim)/Float(dim);
40 check_macro(l == k-1 || l == k || l == k+1, "invalid (k,l)");
41 space Xhs(omega, "P"+to_string(k+1)+"d"),
42 Zh (omega, "P0"),
43 Mht(omega, "trace_n(RT"+to_string(max(k,l))+"d)");
44 trial us(Xhs), u(Xh), zeta(Zh), deltat(Mht), lambda(Mh);
45 test ws(Xhs), w(Xh), xi(Zh), phit(Mht), mu(Mh);
46 auto lh = lazy_integrate (f(dim)*w);
47 auto m = lazy_integrate (u*w);
48 auto as = lazy_integrate (dot(grad_h(us),A(dim)*grad_h(ws)));
49 auto cs = lazy_integrate (pow(h_local(),2)*zeta*xi);
50 auto mt = lazy_integrate (on_local_sides(deltat*phit));
51 auto ct = lazy_integrate (on_local_sides(beta*pow(h_local(),-1)*deltat*phit));
52 auto bs = lazy_integrate (us*xi);
53 auto d = lazy_integrate (u*xi);
54 auto ds = lazy_integrate (us*w);
55 auto dt = lazy_integrate (on_local_sides(u*phit));
56 auto dst= lazy_integrate (on_local_sides(us*phit));
57 auto ac = lazy_integrate (dot(grad_h(u),A(dim)*grad_h(ws))
58 - on_local_sides(u*dot(A(dim)*grad_h(ws),normal())));
59 auto et = lazy_integrate (on_local_sides(mu*deltat));
60 auto es = lazy_integrate (on_local_sides(mu*dot(A(dim)*grad_h(us),normal())));
61 auto inv_cs = inv(cs);
62 auto inv_Ss = inv(as + trans(bs)*inv_cs*bs);
63 auto inv_T = inv(as*inv_Ss*as + trans(bs)*inv_cs*bs);
64 auto R = as*inv_Ss*trans(bs)*inv_cs*d - ac;
65 auto Ac = trans(R)*inv_T*R;
66 auto D = ct*inv(mt)*(dst - dt*inv(m)*ds);
67 auto M0 = inv_Ss - inv_Ss*as*inv_T*as*inv_Ss;
68 auto inv_M = inv(ct + D*M0*trans(D));
69 auto E = trans(dt)*inv(mt)*ct
70 + trans(ac)*inv_T*as*inv_Ss*trans(D)
71 + trans(d)*inv_cs*bs*M0*trans(D);
72 auto As = E*inv_M*trans(E);
73 auto inv_A = inv(Ac + As);
74 auto F = es*inv_T*as*inv_Ss*trans(D)
75 - et*inv(mt)*ct;
76 auto C = es*inv_T*trans(es) + F*inv_M*trans(F);
77 auto B = F*inv_M*trans(E) - es*inv_T*R;
78 form S = C - B*inv_A*trans(B);
79 problem pS (S);
80 field rhs = -B*(inv_A*lh);
81 field lambda_h(Mh, 0);
82 pS.solve (rhs, lambda_h);
83 auto uh = inv_A*(lh - B.trans_mult(lambda_h));
84 auto deltat_h = inv_M*(E.trans_mult(uh) + F.trans_mult(lambda_h));
85 auto vs_h = inv_T*(-as*inv_Ss*D.trans_mult(deltat_h) + R*uh - es.trans_mult(lambda_h));
86 field us_h = inv_Ss*(-as*vs_h - D.trans_mult(deltat_h) + trans(bs)*inv_cs*d*uh);
87 dout << catchmark("us") << us_h
88 << catchmark("u") << field(uh)
89 << catchmark("lambda") << lambda_h;
90}
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
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.
int main()
Definition field2bb.cc:58
check_macro(expr1.have_homogeneous_space(Xh1), "dual(expr1,expr2); expr1 should have homogeneous space. HINT: use dual(interpolate(Xh, expr1),expr2)")
This file is part of Rheolef.
tensor_basic< T > inv(const tensor_basic< T > &a, size_t d)
Definition tensor.cc:219
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 D(const Expr &expr)
D(uh): see the expression page for the full documentation.
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
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
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.
rheolef - reference manual
The sinus product function – right-hand-side and boundary condition for the Poisson problem.
Definition cavity_dg.h:29
Definition leveque.h:25