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mosolov_residue.cc

The Mossolov problem – residue analysis.

The Mossolov problem – residue analysis

#include "rheolef.h"
using namespace std;
using namespace rheolef;
#include "vector_projection.h"
int main(int argc, char**argv) {
environment rheolef(argc,argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-12;
Float Bi, n, r;
field uh, sigma_h;
din >> catchmark("Bi") >> Bi
>> catchmark("n") >> n
>> catchmark("r") >> r
>> catchmark("sigma") >> sigma_h
>> catchmark("u") >> uh;
space Th = sigma_h.get_space();
space Xh = uh.get_space();
trial u (Xh), sigma (Th);
test v (Xh), tau (Th);
form m = integrate(u*v);
form a = integrate(dot(grad(u),grad(v)));
form b = integrate(dot(grad(u),tau));
form mt = integrate(dot(sigma,tau));
integrate_option iopt;
iopt.invert = true;
form inv_mt = integrate(dot(sigma,tau), iopt);
field lh = integrate(2*v);
field grad_uh = inv_mt*(b*uh);
auto c = compose (vector_projection(Bi,n), norm(sigma_h));
field r_sigma_h = lazy_interpolate(Th, grad_uh - c*sigma_h);
field mr_uh = lh - b.trans_mult(sigma_h-r*grad_uh) - r*(a*uh);
mr_uh["boundary"] = 0;
field r_uh (Xh);
problem pm (m);
pm.solve (mr_uh, r_uh);
Float residue_uh = sqrt(m(r_uh,r_uh));
Float residue_sigma_h = sqrt(mt(r_sigma_h,r_sigma_h));
derr << "norm_linf residue(uh) = " << r_uh.max_abs() << endl
<< "norm_l2 residue(uh) = " << residue_uh << endl
<< "norm_linf residue(sigma_h) = " << r_sigma_h.max_abs() << endl
<< "norm_l2 residue(sigma_h) = " << residue_sigma_h << endl;
Float residue = max(residue_uh, residue_sigma_h);
return (residue <= tol) ? 0 : 1;
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
problem
see the problem 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::integrate_option
see the integrate_option page for the full documentation
Definition integrate_option.h:125
rheolef::integrate_option::invert
bool invert
Definition integrate_option.h:168
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::compose
std::enable_if< sizeof...(Exprs)>=3, details::field_expr_v2_nonlinear_node_nary< typenamedetails::function_traits< Function >::functor_type, typenamedetails::field_expr_v2_nonlinear_terminal_wrapper_traits< Exprs >::type... > >::type compose(const Function &f, const Exprs &... exprs)
see the compose page for the full documentation
Definition compose.h:247
rheolef::grad
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(const Expr &expr)
grad(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:930
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::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::norm
T norm(const vec< T, M > &x)
norm(x): see the expression page for the full documentation
Definition vec.h:387
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.
residue
field residue(Float p, const field &uh)
Definition p_laplacian_post.cc:35
rheolef.h
rheolef - reference manual
sigma
Definition mosolov_exact_circle.h:40
u
Definition leveque.h:25
vector_projection
Definition vector_projection.h:26
vector_projection.h
The projection for yield-stress rheologies – vector-valued case for the Mossolov problem.