Rheolef  7.2
an efficient C++ finite element environment
dirichlet_hho_debug.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "sinusprod_dirichlet.h"
29 #include "diffusion_isotropic.h"
30 template <class Expr>
31 void 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 }
37 template <class Expr>
38 void 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 }
45 template <class Expr>
46 void 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 }
54 int 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
Definition: environment.h:121
odiststream: see the diststream page for the full documentation
Definition: diststream.h:137
double Float
see the Float page for the full documentation
Definition: Float.h:143
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:467
form_basic< Float, rheo_default_memory_model > form
Definition: form.h:309
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)
int main(int argc, char **argv)
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
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
Float alpha[pmax+1][pmax+1]
Definition: bdf.icc:28
This file is part of Rheolef.
void put(std::ostream &out, std::string name, const tiny_matrix< T > &a)
Definition: tiny_lu.h:155
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
tensor_basic< T > inv(const tensor_basic< T > &a, size_t d)
Definition: tensor.cc:219
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:211
std::enable_if< details::has_field_rdof_interface< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): 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
std::enable_if< details::has_field_rdof_interface< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::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
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: leveque.h:25