Rheolef  7.2
an efficient C++ finite element environment
 
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diffusion_transport_tensor_dg.cc
Go to the documentation of this file.
1
25#include "rheolef.h"
26using namespace rheolef;
27using namespace std;
29int 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 eps = (argc > 6) ? atof(argv[6]) : 1e-2;
37 Float a = 0;
38 size_t d = omega.dimension();
39 size_t k = Xh.degree();
40 Float eta = (k+1)*(k+d)/Float(d);
41 trial sigma (Xh); test tau (Xh);
42 tensor ma = 0.5*((1-a)*grad_u - (1+a)*trans(grad_u));
43 auto beta_a = sigma*ma + trans(ma)*sigma;
44 form ah = integrate (ddot(grad_h(sigma)*u + beta_a + nu*sigma,tau)
45 + eps*dddot(grad_h(sigma), grad_h(tau)))
46 + integrate ("boundary",
47 max(0, -dot(u,normal()))*ddot(sigma,tau))
48 + integrate ("internal_sides",
49 - dot(u,normal())*ddot(jump(sigma),average(tau))
50 + 0.5*alpha*abs(dot(u,normal()))
51 *ddot(jump(sigma),jump(tau)))
52 + integrate("sides",
53 eps*eta*penalty()*ddot(jump(sigma),jump(tau))
54 - eps*ddot(jump(sigma), average(grad_h(tau )*normal()))
55 - eps*ddot(jump(tau) , average(grad_h(sigma)*normal())));
56 field lh = integrate (ddot(chi(eps,nu,t0),tau))
57 + integrate ("boundary",
58 max(0, -dot(u,normal()))*ddot(sigma_g(nu,t0),tau)
59 + eps*eta*penalty()*ddot(sigma_g(nu,t0),tau)
60 - eps*ddot(sigma_g(nu,t0),grad_h(tau)*normal())
61 + eps*ddot(grad_sigma_g(nu,t0)*normal(),tau));
62 field sigma_h(Xh);
63 problem p (ah);
64 p.solve (lh, sigma_h);
65 dout << catchmark("nu") << nu << endl
66 << catchmark("t0") << t0 << endl
67 << catchmark("sigma") << sigma_h;
68}
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 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
The tensor transport-diffusion benchmark – right-hand-side and exact solution.
int main()
Definition field2bb.cc:58
This file is part of Rheolef.
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
T dddot(const tensor3_basic< T > &a, const tensor3_basic< T > &b)
Definition tensor3.cc:94
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_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
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
details::field_expr_v2_nonlinear_terminal_function< details::penalty_pseudo_function< Float > > penalty()
penalty(): see the expression page for the full documentation
STL namespace.
rheolef - reference manual
Definition eta.h:25
Definition nu.h:26
Definition sphere.icc:25
Definition leveque.h:25