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

The heat equation

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main (int argc, char **argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
size_t n_max = (argc > 2) ? atoi(argv[2]) : 100;
Float delta_t = 0.5/n_max;
space Xh (omega, "P1");
Xh.block ("boundary");
trial u (Xh); test v (Xh);
form a = integrate (u*v + delta_t*dot(grad(u),grad(v)));
problem p (a);
field uh (Xh, 0);
branch event ("t","u");
dout << event (0, uh);
for (size_t n = 1; n <= n_max; n++) {
field rhs = uh + delta_t;
field lh = integrate (rhs*v);
p.solve (lh, uh);
dout << event (n*delta_t, uh);
}
}
form
see the form page for the full documentation
rheolef::dot
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
field
see the field page for the full documentation
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:202
space
see the space page for the full documentation
rheolef::grad
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
Definition: field_expr_terminal.h:911
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25
a
Definition: diffusion_isotropic.h:25
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
test
see the test page for the full documentation
problem
see the problem page for the full documentation
u
Definition: leveque.h:25
Float
see the Float page for the full documentation
branch
see the branch page for the full documentation
u
Float u(const point &x)
Definition: transmission_error.cc:26
mkgeo_ball.n
n
Definition: mkgeo_ball.sh:150
trial
see the test page for the full documentation
main
int main(int argc, char **argv)
Definition: heat.cc:28
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::std
Definition: vec_expr_v2.h:391
geo
see the geo page for the full documentation