Rheolef  7.1
an efficient C++ finite element environment
zalesak_dg.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "zalesak.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  Float tf = u::period(), delta_t = tf/n_max;
38  trial phi (Xh); test xi (Xh);
39  form m = integrate (phi*xi),
40  a0 = integrate (dot(u(),grad_h(phi))*xi)
41  + integrate ("boundary", max(0, -dot(u(),normal()))*phi*xi)
42  + integrate ("internal_sides",
43  - dot(u(),normal())*jump(phi)*average(xi)
44  + 0.5*abs(dot(u(),normal()))*jump(phi)*jump(xi));
45  problem pb;
46  branch event ("t","phi");
47  vector<field> phi_h (p+1);
48  phi_h[0] = phi_h[1] = interpolate (Xh, phi0());
49  dout << event (0, phi_h[0]);
50  for (size_t n = 1; n <= n_max; n++) {
51  Float t = n*delta_t;
52  if (n % 10 == 0) derr << "[" << n << "]";
53  size_t pn = min(n,p);
54  field rhs(Xh, 0);
55  for (size_t i = 1; i <= pn; i++)
56  rhs += (bdf::alpha[pn][i]/delta_t)*phi_h[i];
57  field lh = integrate(rhs*xi)
58  + integrate("boundary", max(0,-dot(u(),normal()))*phi_exact(t)*xi);
59  if (pn <= p) {
60  form an = a0 + (bdf::alpha[pn][0]/delta_t)*m;
61  pb = problem (an);
62  }
63  pb.solve (lh, phi_h[0]);
64  check_macro (phi_h[0].max_abs() < 100, "BDF failed -- HINT: decrease delta_t");
65  if (!strip || n == n_max) dout << event (t, phi_h[0]);
66  for (size_t i = min(p,pn+1); i >= 1; i--)
67  phi_h[i] = phi_h[i-1];
68  }
69  derr << endl;
70 }
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:104
problem_basic< Float > problem
Definition: problem.h:163
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
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.
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_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
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
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
Float u(const point &x)
The Zalesak slotted disk benchmark – the exact solution.
int main(int argc, char **argv)
Definition: zalesak_dg.cc:30