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

The Helmholtz problem on a surface

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "sphere.icc"
int main(int argc, char**argv) {
environment rheolef(argc, argv);
geo gamma (argv[1]);
size_t d = gamma.dimension();
space Wh (gamma, argv[2]);
trial u (Wh); test v (Wh);
form a = integrate (u*v + dot(grad_s(u),grad_s(v)));
field lh = integrate (f(d)*v);
field uh (Wh);
problem p (a);
p.solve (lh, uh);
dout << 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
mkgeo_ball.f
int f
Definition: mkgeo_ball.sh:221
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
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
space
see the space page for the full documentation
rk::gamma
Float gamma[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:70
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25
main
int main(int argc, char **argv)
Definition: helmholtz_s.cc:29
sphere.icc
The level set function for the sphere geometry.
a
Definition: diffusion_isotropic.h:25
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef::grad_s
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_s(const Expr &expr)
grad_s(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:929
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
u
Float u(const point &x)
Definition: transmission_error.cc:26
trial
see the test page for the full documentation
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::std
Definition: vec_expr_v2.h:402
geo
see the geo page for the full documentation