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

The Helmholtz problem on a surface by the banded level-set method

#include "rheolef.h"
using namespace std;
using namespace rheolef;
#include "sphere.icc"
int main (int argc, char**argv) {
environment rheolef(argc, argv);
geo lambda (argv[1]);
size_t d = lambda.dimension();
space Xh (lambda, "P1");
field phi_h = interpolate(Xh, phi);
band gamma_h (phi_h);
field phi_h_band = phi_h [gamma_h.band()];
space Bh (gamma_h.band(), "P1");
Bh.block ("isolated");
Bh.unblock ("zero");
trial u (Bh); test v (Bh);
form a = integrate (gamma_h, u*v + dot(grad_s(u),grad_s(v)));
field lh = integrate (gamma_h, f(d)*v);
vector<field> b (gamma_h.n_connected_component());
vector<Float> z (gamma_h.n_connected_component(), 0);
for (size_t i = 0; i < b.size(); i++) {
const domain& cci = gamma_h.band() ["cc"+itos(i)];
field phi_h_cci (Bh, 0);
phi_h_cci [cci] = phi_h_band [cci];
b[i] = phi_h_cci;
}
form A = {{ a, trans(b) },
{ b, 0 }};
field Fh = { lh, z };
A.set_symmetry(true);
problem pa (A);
field Uh (Fh.get_space(), 0);
pa.solve (Fh, Uh);
dout << catchmark("phi") << phi_h
<< catchmark("u") << Uh[0];
}
field lh(Float epsilon, Float t, const test &v)
see the band 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 space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
int main(int argc, char **argv)
rheolef::details::is_vec dot
This file is part of Rheolef.
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
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
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
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef - reference manual
The level set function for the sphere geometry.
Definition: phi.h:25
Definition: leveque.h:25
Float u(const point &x)