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reconstruction_hho_v2.cc

The hybrid high order method – reconstruction operator.

The hybrid high order method – reconstruction operator

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "sinusprod.h"
#include "diffusion_isotropic.h"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
string Pkd = (argc > 2) ? argv[2] : "P0",
Pld = (argc > 3) ? argv[3] : Pkd;
space Xh (omega, Pld),
Mh (omega["sides"], Pkd);
size_t k = Xh.degree(), l = Xh.degree(), d = omega.dimension();
check_macro(l == k-1 || l == k || l == k+1,
"invalid (k,l) = ("<<k<<","<<l<<")");
space Xhs(omega, "P"+to_string(k+1)+"d"),
Zh (omega, "P0");
trial u(Xh), lambda(Mh), us(Xhs), zeta (Zh);
test v(Xh), mu (Mh), vs(Xhs), xi (Zh);
form as = lazy_integrate (dot(grad_h(us),A(d)*grad_h(vs)));
form bs = lazy_integrate (us*xi);
auto cs = lazy_integrate (pow(h_local(),2)*zeta*xi);
auto m = lazy_integrate (u*v);
form ms = lazy_integrate (lambda*mu);
form inv_m = inv(m);
form inv_cs = inv(cs);
form ss = as + trans(bs)*inv_cs*bs;
field llh = integrate(u_exact(d)*v);
field rhs = integrate(u_exact(d)*mu);
field pi_Xh_u = inv_m*llh;
field pi_Mh_lambda(Mh);
problem pms (ms);
pms.solve (rhs, pi_Mh_lambda);
field lh = integrate (dot(grad_h(pi_Xh_u),A(d)*grad_h(vs))
+ on_local_sides((pi_Mh_lambda-pi_Xh_u)
*dot(normal(),A(d)*grad_h(vs))));
field kh = integrate (pi_Xh_u*xi);
field rh = lh + bs.trans_mult(inv_cs*kh);
problem pss (ss);
field us_h (Xhs, 0);
pss.solve (rh, us_h);
field zeta_h = inv_cs*(bs*us_h - kh);
dout << catchmark("us") << us_h
<< catchmark("zeta") << zeta_h;
}
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::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
diffusion_isotropic.h
Tensor diffusion – isotropic case.
main
int main()
Definition field2bb.cc:58
check_macro
check_macro(expr1.have_homogeneous_space(Xh1), "dual(expr1,expr2); expr1 should have homogeneous space. HINT: use dual(interpolate(Xh, expr1),expr2)")
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
std
STL namespace.
d
size_t d
Definition neumann-laplace-lambda.cc:28
rheolef.h
rheolef - reference manual
sinusprod.h
The sinus product function.
A
Definition diffusion_isotropic.h:25
lambda
Definition yield_slip_circle.h:34
u_exact
Definition interpolate_RTk_polynom.icc:125
u
Definition leveque.h:25