Rheolef  7.2
an efficient C++ finite element environment
p_laplacian_fixed_point.cc

The p-Laplacian problem by the fixed-point method.

The p-Laplacian problem by the fixed-point method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "eta.h"
#include "dirichlet.icc"
int main(int argc, char**argv) {
environment rheolef (argc,argv);
geo omega (argv[1]);
string approx = (argc > 2) ? argv[2] : "P1";
Float p = (argc > 3) ? atof(argv[3]) : 1.5;
Float w = (argc > 4) ? (is_float(argv[4]) ? atof(argv[4]) :2/p) :1;
Float tol = (argc > 5) ? atof(argv[5]) : 1e5*eps;
size_t max_it = (argc > 6) ? atoi(argv[6]) : 500;
derr << "# P-Laplacian problem by fixed-point:" << endl
<< "# geo = " << omega.name() << endl
<< "# approx = " << approx << endl
<< "# p = " << p << endl
<< "# w = " << w << endl
<< "# tol = " << tol << endl;
space Xh (omega, approx);
Xh.block ("boundary");
trial u (Xh); test v (Xh);
form m = integrate (u*v);
problem pm (m);
field uh (Xh), uh_star (Xh, 0.);
uh["boundary"] = uh_star["boundary"] = 0;
dirichlet (lh, uh);
derr << "# n r v" << endl;
Float r = 1, r0 = 1;
size_t n = 0;
do {
field mrh = a*uh - lh;
field rh (Xh, 0);
pm.solve (mrh, rh);
r = rh.max_abs();
if (n == 0) { r0 = r; }
Float v = (n == 0) ? 0 : log10(r0/r)/n;
derr << n << " " << r << " " << v << endl;
if (r <= tol || n++ >= max_it) break;
problem p (a);
p.solve (lh, uh_star);
uh = w*uh_star + (1-w)*uh;
} while (true);
dout << catchmark("p") << p << endl
<< catchmark("u") << uh;
return (r <= tol) ? 0 : 1;
}
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
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.
class rheolef::details::field_expr_v2_nonlinear_node_unary compose
rheolef::details::is_vec dot
This file is part of Rheolef.
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(const Expr &expr)
grad(uh): see the expression page for the full documentation
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
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
bool is_float(const string &s)
is_float: see the rheostream page for the full documentation
Definition: rheostream.cc:480
STL namespace.
int main(int argc, char **argv)
rheolef - reference manual
Definition: eta.h:25
Definition: sphere.icc:25
Definition: leveque.h:25
Float epsilon