Rheolef  7.1
an efficient C++ finite element environment
dirichlet_hho.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "dirichlet_homogeneous.h"
29 #include "diffusion_isotropic.h"
30 int 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  Float beta = (argc > 4) ? atof(argv[4]) : 1;
36  space Xh (omega, Pld),
37  Mh (omega["sides"], Pkd);
38  Mh.block("boundary");
39  size_t k = Xh.degree(), l = Mh.degree(), d = omega.dimension();
40  check_macro(l == k-1 || l == k || l == k+1,
41  "invalid (k,l) = ("<<k<<","<<l<<")");
42  space Xhs(omega, "P"+itos(k+1)+"d"),
43  Zh (omega, "P0"),
44  Mht(omega, "trace(P"+itos(k)+"d)");
45  space Yh = Xh*Xhs*Xh*Mht*Zh;
46  trial x(Yh), lambda(Mh);
47  test y(Yh), mu(Mh);
48  auto u = x[0], us = x[1], ut = x[2], deltat = x[3], zeta = x[4];
49  auto v = y[0], vs = y[1], vt = y[2], gammat = y[3], xi = y[4];
50  integrate_option iopt;
51  iopt.invert = true;
52  form inv_a = integrate(dot(grad_h(us),a(d)*grad_h(vs))
53  + dot(grad_h(us)-grad_h(u),a(d)*(grad_h(vs)-grad_h(v)))
54  + (us-u)*xi + (vs-v)*zeta + (ut-us)*(vt-vs)
55  + on_local_sides(beta/h_local()*deltat*gammat
56  + u*dot(a(d)*grad_h(vs),normal())
57  + v*dot(a(d)*grad_h(us),normal())
58  + (deltat - us + ut)*(gammat - vs + vt)), iopt);
59  form b = integrate(omega,on_local_sides(-mu*dot(a(d)*grad_h(us),normal())));
60  // TODO: remove omega, autodetect it ?
61  field lh = integrate (f(d)*v);
62  // TODO: f -> -f ? check the FV...
63  field lambda_h(Mh,0);
64  form s = b*inv_a*trans(b);
65  field rh = b*(inv_a*lh);
66  problem p (s);
67  p.solve (rh, lambda_h);
68  field xh = inv_a*(lh - b.trans_mult(lambda_h));
69  dout << catchmark("beta") << beta << endl
70  << catchmark("u") << xh[0]
71  << catchmark("us") << xh[1]
72  << catchmark("ut") << xh[2]
73  << catchmark("delta") << xh[3]
74  << catchmark("zeta") << xh[4]
75  << catchmark("lambda") << lambda_h;
76 }
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:115
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
Tensor diffusion – isotropic case.
int main(int argc, char **argv)
The Poisson problem with homogeneous Dirichlet boundary conditions – right-hand-side and boundary con...
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
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_convertible< 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_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
std::string itos(std::string::size_type i)
itos: see the rheostream 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
Float beta[][pmax+1]
rheolef - reference manual
Definition: sphere.icc:25
Definition: leveque.h:25