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laplace_s.cc

The Poisson problem on a surface.

The Poisson problem on a surface

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "torus.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 (dot(grad_s(u),grad_s(v)));
field b = integrate(v);
field lh = integrate (f(d)*v);
form A = {{ a, b },
{ trans(b), 0 }};
field Bh = { lh, 0 };
field Uh (Bh.get_space(), 0);
A.set_symmetry(true);
problem pa (A);
pa.solve (Bh, Uh);
dout << Uh[0];
}
f
point f(const Float &u)
Definition burgers.icc:25
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
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::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
main
int main()
Definition field2bb.cc:58
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
rheolef::grad_s
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_s(const Expr &expr)
grad_s(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:948
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::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition csr.h:455
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.
d
size_t d
Definition neumann-laplace-lambda.cc:28
rheolef.h
rheolef - reference manual
A
Definition diffusion_isotropic.h:25
u
Definition leveque.h:25
torus.icc
The torus benchmark – level set, right-hand-side and exact solution.