Rheolef  7.2
an efficient C++ finite element environment
 
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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"
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;
}
field lh(Float epsilon, Float t, const test &v)
see the field page for the full documentation
see the form page for the full documentation
see the geo page for the full documentation
see the problem page for the full documentation
see the catchmark page for the full documentation
Definition catchmark.h:67
see the environment page for the full documentation
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
Tensor diffusion – isotropic case.
int main()
Definition field2bb.cc:58
check_macro(expr1.have_homogeneous_space(Xh1), "dual(expr1,expr2); expr1 should have homogeneous space. HINT: use dual(interpolate(Xh, expr1),expr2)")
This file is part of Rheolef.
STL namespace.
rheolef - reference manual
The sinus product function.
Definition leveque.h:25