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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]);
Float eps = std::numeric_limits<Float>::epsilon();
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;
field lh = integrate (v);
dirichlet (lh, uh);
derr << "# n r v" << endl;
Float r = 1, r0 = 1;
size_t n = 0;
do {
form a = integrate(compose(eta(p),norm2(grad(uh)))*dot(grad(u),grad(v)));
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;
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition environment.h:121
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
u
point u(const point &x)
Definition diffusion_transport_tensor_exact.icc:25
dirichlet.icc
The Poisson problem with homogeneous Dirichlet boundary condition – solver function.
dirichlet
void dirichlet(const field &lh, field &uh)
Definition dirichlet.icc:25
eta.h
The p-Laplacian problem – the eta function.
main
int main()
Definition field2bb.cc:58
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
rheolef::compose
std::enable_if< sizeof...(Exprs)>=3, details::field_expr_v2_nonlinear_node_nary< typenamedetails::function_traits< Function >::functor_type, typenamedetails::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
rheolef::grad
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
Definition field_expr_terminal.h:930
rheolef::norm2
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition vec.h:379
rheolef::integrate
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
rheolef::is_float
bool is_float(const string &s)
is_float: see the rheostream page for the full documentation
Definition rheostream.cc:480
rheolef::dot
rheolef::std::enable_if< details::is_vec_expr_v2_arg< Expr1 >::value &&details::is_vec_expr_v2_arg< Expr2 >::value, promote< Expr1::float_type, Expr2::float_type >::type > type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
Definition vec_expr_v2.h:415
std
STL namespace.
rheolef.h
rheolef - reference manual
eta
Definition eta.h:25
p
Definition sphere.icc:25
u
Definition leveque.h:25