Rheolef  7.2
an efficient C++ finite element environment
 
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dirichlet_hho_debug.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"
30template <class Expr>
31void mtx (const Expr& a_expr, string a_name) {
32 form a = a_expr;
33 odiststream out (a_name+".mtx",io::nogz);
34 out << setbasename(a_name) << a.uu();
35 out.close();
36}
37template <class Expr>
38void put (odiststream& out, const Expr& a_expr, string a_name) {
39 trace_macro(a_name<<"...");
40 form a = a_expr;
41 trace_macro(a_name<<" done");
42 out << matlab
43 << setbasename(a_name) << a.uu();
44}
45template <class Expr>
46void sdp (const Expr& a_expr, string a_name) {
47 odiststream out (a_name+".m",io::nogz);
48 put (out, a_expr, a_name);
49 out << "eig_"<<a_name<<"=eig("<<a_name<<")" <<endl
50 << "det_"<<a_name<<"=det("<<a_name<<")" <<endl
51 ;
52 out.close();
53}
54int main(int argc, char**argv) {
55 environment rheolef (argc, argv);
56 geo omega (argv[1]);
57 string Pkd = (argc > 2) ? argv[2] : "P1d",
58 Pld = (argc > 3) ? argv[3] : Pkd;
59 space Xh (omega, Pld),
60 Mh (omega["sides"], Pkd);
61 Mh.block("boundary");
62 size_t k = Xh.degree(), l = Mh.degree(), kl = max(k,l), dim = omega.dimension();
63 Float alpha = 1;
64 Float beta = (argc > 4) ? atof(argv[4]) : 10*(k+1)*(k+dim)/Float(dim);
65 check_macro(l == k-1 || l == k || l == k+1,
66 "invalid (k,l) = ("<<k<<","<<l<<")");
67 space Xhs(omega, "P"+to_string(k+1)+"d"),
68 Zh (omega, "P0"),
69 Mht(omega, "trace_n(RT"+to_string(kl)+"d)");
70 trial us(Xhs), u(Xh), zeta(Zh), deltat(Mht), lambda(Mh);
71 test ws(Xhs), w(Xh), xi(Zh), phit(Mht), mu(Mh);
72 field lh = integrate (f(dim)*w);
73 auto m = lazy_integrate (u*w);
74 auto as = lazy_integrate (dot(grad_h(us),A(dim)*grad_h(ws)));
75 auto cs = lazy_integrate (alpha*pow(h_local(),2)*zeta*xi);
76 auto mt = lazy_integrate (on_local_sides(deltat*phit));
77 auto ct = lazy_integrate (on_local_sides(beta*pow(h_local(),-1)*deltat*phit));
78 auto bs = lazy_integrate (us*xi);
79 auto d = lazy_integrate (u*xi);
80 auto ds = lazy_integrate (us*w);
81 auto dt = lazy_integrate (on_local_sides(u*phit));
82 auto dst= lazy_integrate (on_local_sides(us*phit));
83 auto ac = lazy_integrate (dot(grad_h(u),A(dim)*grad_h(ws))
84 - on_local_sides(u*dot(A(dim)*grad_h(ws),normal())));
85 auto et = lazy_integrate (on_local_sides(mu*deltat));
86 auto es = lazy_integrate (on_local_sides(mu*dot(A(dim)*grad_h(us),normal())));
87 auto inv_cs = inv(cs);
88 auto inv_Ss = inv(as + trans(bs)*inv_cs*bs);
89 auto inv_T = inv(as*inv_Ss*as + trans(bs)*inv_cs*bs);
90 auto R = as*inv_Ss*trans(bs)*inv_cs*d - ac;
91 auto Ac = trans(R)*inv_T*R;
92 auto D = ct*inv(mt)*(dst - dt*inv(m)*ds);
93 auto M0 = inv_Ss - inv_Ss*as*inv_T*as*inv_Ss;
94 auto inv_M = inv(ct + D*M0*trans(D));
95 // TODO: tester si Ei==0 avec E=E1+E2+E3
96 auto E = trans(dt)*inv(mt)*ct
97 + trans(ac)*inv_T*as*inv_Ss*trans(D)
98 + trans(d)*inv_cs*bs*M0*trans(D);
99 auto As = E*inv_M*trans(E);
100 auto inv_A = inv(Ac + As);
101 auto F = es*inv_T*as*inv_Ss*trans(D)
102 - et*inv(mt)*ct;
103 auto C = es*inv_T*trans(es) + F*inv_M*trans(F);
104 auto B = F*inv_M*trans(E) - es*inv_T*R;
105 form S = C - B*inv_A*trans(B);
106#ifdef TO_CLEAN
107 sdp(A, "A");
108 sdp(C, "C");
109 sdp(S, "S");
110#endif // TO_CLEAN
111 problem pS (S);
112 field rhs = -form(B*inv_A)*lh; // TODO: lazy_form_field_expr
113 field lambda_h(Mh, 0);
114 pS.solve (rhs, lambda_h);
115 field uh = form(inv_A)*(lh - form(B).trans_mult(lambda_h));
116 field deltat_h = form(inv_M)*(form(E).trans_mult(uh) + form(F).trans_mult(lambda_h));
117 field vs_h = form(inv_T)*(-form(as*inv_Ss*trans(D))*deltat_h + form(R)*uh - form(es).trans_mult(lambda_h));
118 field us_h = form(inv_Ss)*(-form(as)*vs_h - form(D).trans_mult(deltat_h) + form(trans(bs)*inv_cs*d)*uh);
119 dout << catchmark("beta") << beta << endl
120 << catchmark("us") << us_h
121 << catchmark("u") << uh
122 << catchmark("lambda") << lambda_h;
123}
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
odiststream: see the diststream page for the full documentation
Definition diststream.h:137
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.
void sdp(const Expr &a_expr, string a_name)
void mtx(const Expr &a_expr, string a_name)
#define trace_macro(message)
Definition dis_macros.h:111
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)")
verbose clean transpose logscale grid shrink ball stereo iso volume skipvtk deformation fastfieldload lattice reader_on_stdin color format format format format format format format format format format format format format format format matlab
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
void put(std::ostream &out, std::string name, const tiny_matrix< T > &a)
Definition tiny_lu.h:155
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
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