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laplace_band_error.cc
Go to the documentation of this file.
#include "rheolef.h"
using namespace std;
using namespace rheolef;
#include "torus.icc"
int main (int argc, char**argv) {
environment rheolef (argc, argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-7;
bool do_dump = (argc > 2) ? true : false;
field phi_h;
din >> catchmark("phi") >> phi_h;
const space& Xh = phi_h.get_space();
band gamma_h (phi_h);
space Bh (gamma_h.band(), "P1");
field uh(Bh);
din >> catchmark("u") >> uh;
trial u (Bh); test v (Bh);
form m = lazy_integrate (gamma_h, u*v);
form a = lazy_integrate (gamma_h, dot(grad_s(u),grad_s(v)));
size_t d = Bh.get_geo().dimension();
field pi_h_u = lazy_interpolate(Bh, u_exact(d));
field eh = pi_h_u - uh;
field phi_h_band = phi_h [gamma_h.band()];
Float c1 = m(eh,phi_h_band)/m(phi_h_band,phi_h_band);
field one (Bh, 1);
Float meas_gamma = m(one,one);
Float c2 = m(one,eh)/meas_gamma;
eh = eh - c1*phi_h_band - c2*one;
Float err_l2 = sqrt(m(eh,eh));
Float err_h1 = sqrt(a(eh,eh));
derr << "err_l2 = " << err_l2 << endl
<< "err_h1 = " << err_h1 << endl;
if (do_dump) {
dout << catchmark ("u") << uh
<< catchmark ("ue") << pi_h_u
<< catchmark ("eh") << eh;
}
return (err_l2 < tol && err_h1 < tol) ? 0 : 1;
}
Float
see the Float page for the full documentation
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
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
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::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::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
u
Definition leveque.h:25
u_exact
g u_exact
Definition taylor_exact.h:26
torus.icc
The torus benchmark – level set, right-hand-side and exact solution.