Rheolef  7.2
an efficient C++ finite element environment
leveque_dg.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "leveque.h"
29 #include "bdf.icc"
30 int main(int argc, char**argv) {
31  environment rheolef (argc, argv);
32  geo omega (argv[1]);
33  space Xh (omega, argv[2]);
34  size_t n_max = (argc > 3) ? atoi(argv[3]) : 1000;
35  size_t strip = (argc > 4) ? string(argv[4]) == "true" : false;
36  size_t p = (argc > 5) ? atoi(argv[5]) : min(Xh.degree()+1,bdf::pmax);
37  size_t d = omega.dimension();
38  Float tf = u::period(), delta_t = tf/n_max;
39  trial phi (Xh); test xi (Xh);
40  branch event ("t","phi");
41  vector<field> phi_h (p+1);
42  phi_h[0] = phi_h[1] = lazy_interpolate (Xh, phi0(d));
43  dout << event (0, phi_h[0]);
44  for (size_t n = 1; n <= n_max; n++) {
45  Float t = n*delta_t;
46  if (n % 10 == 0) derr << "[" << n << "]";
47  size_t pn = min(n,p);
48  form an = integrate ((bdf::alpha[pn][0]/delta_t*phi + dot(u(d,t),grad_h(phi)))*xi)
49  + integrate ("internal_sides",
50  - dot(u(d,t),normal())*jump(phi)*average(xi)
51  + 0.5*abs(dot(u(d,t),normal()))*jump(phi)*jump(xi));
52  field rhs(Xh, 0);
53  for (size_t i = 1; i <= pn; i++)
54  rhs += (bdf::alpha[pn][i]/delta_t)*phi_h[i];
55  field lh = integrate(rhs*xi);
56  problem pb (an);
57  pb.solve (lh, phi_h[0]);
58  check_macro (phi_h[0].max_abs() < 100, "BDF failed -- HINT: decrease delta_t");
59  if (!strip || n == n_max) dout << event (t, phi_h[0]);
60  for (size_t i = min(p,pn+1); i >= 1; i--)
61  phi_h[i] = phi_h[i-1];
62  }
63  derr << endl;
64 }
BDF(p) backward differentiation formula – coefficients.
field lh(Float epsilon, Float t, const test &v)
Float phi(const point &nu, Float a, Float b)
see the Float page for the full documentation
see the branch 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 environment page for the full documentation
Definition: environment.h:121
rheolef::space_base_rep< T, M > t
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:467
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:473
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
point u(const point &x)
The Leveque benchmark – function definition.
int main(int argc, char **argv)
Definition: leveque_dg.cc:30
Float alpha[pmax+1][pmax+1]
Definition: bdf.icc:28
constexpr size_t pmax
Definition: bdf.icc:26
T max_abs(const T &x)
This file is part of Rheolef.
field_basic< T, M > lazy_interpolate(const space_basic< T, M > &X2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: field.h:871
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
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: sphere.icc:25
Definition: leveque.h:37
Definition: phi.h:25
static Float period()
Definition: leveque.h:32