Rheolef  7.2
an efficient C++ finite element environment
p_laplacian_fixed_point.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "eta.h"
29 #include "dirichlet.icc"
30 int main(int argc, char**argv) {
31  environment rheolef (argc,argv);
32  geo omega (argv[1]);
34  string approx = (argc > 2) ? argv[2] : "P1";
35  Float p = (argc > 3) ? atof(argv[3]) : 1.5;
36  Float w = (argc > 4) ? (is_float(argv[4]) ? atof(argv[4]) :2/p) :1;
37  Float tol = (argc > 5) ? atof(argv[5]) : 1e5*eps;
38  size_t max_it = (argc > 6) ? atoi(argv[6]) : 500;
39  derr << "# P-Laplacian problem by fixed-point:" << endl
40  << "# geo = " << omega.name() << endl
41  << "# approx = " << approx << endl
42  << "# p = " << p << endl
43  << "# w = " << w << endl
44  << "# tol = " << tol << endl;
45  space Xh (omega, approx);
46  Xh.block ("boundary");
47  trial u (Xh); test v (Xh);
48  form m = integrate (u*v);
49  problem pm (m);
50  field uh (Xh), uh_star (Xh, 0.);
51  uh["boundary"] = uh_star["boundary"] = 0;
52  field lh = integrate (v);
53  dirichlet (lh, uh);
54  derr << "# n r v" << endl;
55  Float r = 1, r0 = 1;
56  size_t n = 0;
57  do {
58  form a = integrate(compose(eta(p),norm2(grad(uh)))*dot(grad(u),grad(v)));
59  field mrh = a*uh - lh;
60  field rh (Xh, 0);
61  pm.solve (mrh, rh);
62  r = rh.max_abs();
63  if (n == 0) { r0 = r; }
64  Float v = (n == 0) ? 0 : log10(r0/r)/n;
65  derr << n << " " << r << " " << v << endl;
66  if (r <= tol || n++ >= max_it) break;
67  problem p (a);
68  p.solve (lh, uh_star);
69  uh = w*uh_star + (1-w)*uh;
70  } while (true);
71  dout << catchmark("p") << p << endl
72  << catchmark("u") << uh;
73  return (r <= tol) ? 0 : 1;
74 }
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
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 Poisson problem with homogeneous Dirichlet boundary condition – solver function.
void dirichlet(const field &lh, field &uh)
Definition: dirichlet.icc:25
The p-Laplacian problem – the eta function.
This file is part of Rheolef.
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(const Expr &expr)
grad(uh): see the expression page for the full documentation
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
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
bool is_float(const string &s)
is_float: see the rheostream page for the full documentation
Definition: rheostream.cc:480
details::field_expr_v2_nonlinear_node_nary< typename details::function_traits< Function >::functor_type,typename details::field_expr_v2_nonlinear_terminal_wrapper_traits< Exprs >::type... > ::type compose(const Function &f, const Exprs &... exprs)
see the compose page for the full documentation
Definition: compose.h:247
int main(int argc, char **argv)
rheolef - reference manual
Definition: eta.h:25
Definition: sphere.icc:25
Definition: leveque.h:25
Float epsilon