Rheolef  7.1
an efficient C++ finite element environment
p_laplacian_fixed_point.cc

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
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
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.
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(const Expr &expr)
grad(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
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:476
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:246
int main(int argc, char **argv)
rheolef - reference manual
Definition: eta.h:25
Definition: sphere.icc:25
Definition: leveque.h:25
Float u(const point &x)
Float epsilon