mosolov_residue.cc

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 = 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;
}
form
see the form page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
field
see the field page for the full documentation
residue
field residue(Float p, const field &uh)
Definition: p_laplacian_post.cc:35
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:202
space
see the space page for the full documentation
vector_projection
Definition: vector_projection.h:26
mkgeo_ball.c
c
Definition: mkgeo_ball.sh:153
rheolef::grad
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(const Expr &expr)
grad(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:911
rheolef::details::compose
class rheolef::details::field_expr_v2_nonlinear_node_unary compose
rheolef::norm
T norm(const vec< T, M > &x)
norm(x): see the expression page for the full documentation
Definition: vec.h:387
rheolef.h
rheolef - reference manual
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition: integrate_option.h:125
a
Definition: diffusion_isotropic.h:25
rheolef::interpolate
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
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
mkgeo_sector.m
m
Definition: mkgeo_sector.sh:118
sigma
Definition: mosolov_exact_circle.h:40
vector_projection.h
The projection for yield-stress rheologies – vector-valued case for the Mossolov problem.
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::integrate_option::invert
bool invert
Definition: integrate_option.h:168
test
see the test page for the full documentation
problem
see the problem page for the full documentation
u
Definition: leveque.h:25
rheolef::din
idiststream din(cin)
see the diststream page for the full documentation
Float
see the Float page for the full documentation
u
Float u(const point &x)
Definition: transmission_error.cc:26
mkgeo_ball.b
b
Definition: mkgeo_ball.sh:152
mkgeo_ball.n
n
Definition: mkgeo_ball.sh:150
trial
see the test page for the full documentation
main
int main(int argc, char **argv)
Definition: mosolov_residue.cc:29
rheolef::details::dot
rheolef::details::is_vec dot