Rheolef  7.2
an efficient C++ finite element environment
transport_tensor_dg.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
29 int main(int argc, char**argv) {
30  environment rheolef (argc, argv);
31  geo omega (argv[1]);
32  space Xh (omega, argv[2], "tensor");
33  Float alpha = (argc > 3) ? atof(argv[3]) : 1;
34  Float nu = (argc > 4) ? atof(argv[4]) : 3;
35  Float t0 = (argc > 5) ? atof(argv[5]) : acos(-1.)/8;
36  Float a = 0;
37  trial sigma (Xh); test tau (Xh);
38  tensor ma = 0.5*((1-a)*grad_u - (1+a)*trans(grad_u));
39  auto beta_a = sigma*ma + trans(ma)*sigma;
40  form ah = integrate (ddot(grad_h(sigma)*u + beta_a + nu*sigma,tau))
41  + integrate ("boundary",
42  max(0, -dot(u,normal()))*ddot(sigma,tau))
43  + integrate ("internal_sides",
44  - dot(u,normal())*ddot(jump(sigma),average(tau))
45  + 0.5*alpha*abs(dot(u,normal()))
46  *ddot(jump(sigma),jump(tau)));
47  field lh = integrate (ddot(chi(nu,t0),tau))
48  + integrate ("boundary",
49  max(0, -dot(u,normal()))*ddot(sigma_g(nu,t0),tau));
50  field sigma_h(Xh);
51  problem p (ah);
52  p.solve (lh, sigma_h);
53  dout << catchmark("nu") << nu << endl
54  << catchmark("t0") << t0 << endl
55  << catchmark("sigma") << sigma_h;
56 }
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 dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:467
see the space page for the full documentation
see the tensor page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
sigma_exact sigma_g
Float alpha[pmax+1][pmax+1]
Definition: bdf.icc:28
This file is part of Rheolef.
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_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
T ddot(const tensor_basic< T > &a, const tensor_basic< T > &b)
ddot(x,y): see the expression page for the full documentation
Definition: tensor.cc:278
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
rheolef - reference manual
Definition: nu.h:26
Definition: sphere.icc:25
Definition: leveque.h:25
int main(int argc, char **argv)
The tensorial transport benchmark – right-hand-side and exact solution.