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helmholtz_band_iterative.cc

The Helmholtz problem on a surface by the banded level-set method – iterative solver.

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

#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 = lazy_interpolate(Xh, phi);
band gamma_h (phi_h);
space Bh (gamma_h.band(), "P1");
trial u (Bh); test v (Bh);
form a = lazy_integrate (gamma_h, u*v + dot(grad_s(u),grad_s(v)));
field lh = lazy_integrate (gamma_h, f(d)*v);
field uh (Bh,0);
solver_option sopt;
sopt.max_iter = 10000;
sopt.tol = 1e-10;
minres (a.uu(), uh.set_u(), lh.u(), eye(), sopt);
dout << catchmark("phi") << phi_h
<< catchmark("u") << uh;
}
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
band
see the band 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
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
rheolef::solver_option
see the solver_option page for the full documentation
Definition solver_option.h:155
rheolef::solver_option::max_iter
size_type max_iter
Definition solver_option.h:161
rheolef::solver_option::tol
Float tol
Definition solver_option.h:160
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::minres
int minres(const Matrix &A, Vector &x, const Vector &Mb, const Preconditioner &M, const solver_option &sopt=solver_option())
Definition minres.h:100
rheolef::lazy_interpolate
field_basic< T, M > lazy_interpolate(const space_basic< T, M > &X2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition field.h:871
rheolef::eye
solver_basic< Float > eye()
see the eye page for the full documentation
Definition eye.h:74
rheolef::lazy_integrate
std::enable_if< details::is_field_expr_quadrature_arg< Expr >::value, details::field_lazy_terminal_integrate< Expr > >::type lazy_integrate(const typename Expr::geo_type &domain, const Expr &expr, const integrate_option &iopt=integrate_option())
see the integrate page for the full documentation
Definition field_lazy_terminal.h:588
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
sphere.icc
The level set function for the sphere geometry.
lambda
Definition yield_slip_circle.h:34
phi
Definition phi.h:25
u
Definition leveque.h:25