Rheolef  7.2
an efficient C++ finite element environment
dirichlet_hho.cc

The Poisson problem by the hybrid high order method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
string Pkd = (argc > 2) ? argv[2] : "P1d",
Pld = (argc > 3) ? argv[3] : Pkd;
space Xh (omega, Pld),
Mh (omega["sides"], Pkd);
Mh.block("boundary");
size_t k = Mh.degree(), l = Xh.degree(), dim = omega.dimension();
Float beta = (argc > 4) ? atof(argv[4]) : 10*(k+1)*(k+dim)/Float(dim);
check_macro(l == k-1 || l == k || l == k+1, "invalid (k,l)");
space Xhs(omega, "P"+to_string(k+1)+"d"),
Zh (omega, "P0"),
Mht(omega, "trace_n(RT"+to_string(max(k,l))+"d)");
trial us(Xhs), u(Xh), zeta(Zh), deltat(Mht), lambda(Mh);
test ws(Xhs), w(Xh), xi(Zh), phit(Mht), mu(Mh);
auto lh = lazy_integrate (f(dim)*w);
auto m = lazy_integrate (u*w);
auto as = lazy_integrate (dot(grad_h(us),A(dim)*grad_h(ws)));
auto cs = lazy_integrate (pow(h_local(),2)*zeta*xi);
auto mt = lazy_integrate (on_local_sides(deltat*phit));
auto ct = lazy_integrate (on_local_sides(beta*pow(h_local(),-1)*deltat*phit));
auto bs = lazy_integrate (us*xi);
auto d = lazy_integrate (u*xi);
auto ds = lazy_integrate (us*w);
auto dt = lazy_integrate (on_local_sides(u*phit));
auto dst= lazy_integrate (on_local_sides(us*phit));
auto ac = lazy_integrate (dot(grad_h(u),A(dim)*grad_h(ws))
auto et = lazy_integrate (on_local_sides(mu*deltat));
auto inv_cs = inv(cs);
auto inv_Ss = inv(as + trans(bs)*inv_cs*bs);
auto inv_T = inv(as*inv_Ss*as + trans(bs)*inv_cs*bs);
auto R = as*inv_Ss*trans(bs)*inv_cs*d - ac;
auto Ac = trans(R)*inv_T*R;
auto D = ct*inv(mt)*(dst - dt*inv(m)*ds);
auto M0 = inv_Ss - inv_Ss*as*inv_T*as*inv_Ss;
auto inv_M = inv(ct + D*M0*trans(D));
auto E = trans(dt)*inv(mt)*ct
+ trans(ac)*inv_T*as*inv_Ss*trans(D)
+ trans(d)*inv_cs*bs*M0*trans(D);
auto As = E*inv_M*trans(E);
auto inv_A = inv(Ac + As);
auto F = es*inv_T*as*inv_Ss*trans(D)
- et*inv(mt)*ct;
auto C = es*inv_T*trans(es) + F*inv_M*trans(F);
auto B = F*inv_M*trans(E) - es*inv_T*R;
form S = C - B*inv_A*trans(B);
problem pS (S);
field rhs = -B*(inv_A*lh);
field lambda_h(Mh, 0);
pS.solve (rhs, lambda_h);
auto uh = inv_A*(lh - B.trans_mult(lambda_h));
auto deltat_h = inv_M*(E.trans_mult(uh) + F.trans_mult(lambda_h));
auto vs_h = inv_T*(-as*inv_Ss*D.trans_mult(deltat_h) + R*uh - es.trans_mult(lambda_h));
field us_h = inv_Ss*(-as*vs_h - D.trans_mult(deltat_h) + trans(bs)*inv_cs*d*uh);
dout << catchmark("us") << us_h
<< catchmark("u") << field(uh)
<< catchmark("lambda") << lambda_h;
}
field lh(Float epsilon, Float t, const test &v)
see the Float page for the full documentation
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
double Float
see the Float page for the full documentation
Definition: Float.h:143
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:467
field_basic< Float > field
see the field page for the full documentation
Definition: field.h:511
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.
point u(const point &x)
int main(int argc, char **argv)
This file is part of Rheolef.
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
tensor_basic< T > inv(const tensor_basic< T > &a, size_t d)
Definition: tensor.cc:219
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
std::enable_if< details::is_field_expr_v2_variational_arg< Expr >::value,details::field_expr_quadrature_on_sides< Expr > >::type on_local_sides(const Expr &expr)
on_local_sides(expr): see the expression page for the full documentation
std::enable_if< details::has_field_rdof_interface< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
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
std::enable_if< details::has_field_rdof_interface< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type D(const Expr &expr)
D(uh): see the expression page for the full documentation.
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Float beta[][pmax+1]
rheolef - reference manual
The sinus product function – right-hand-side and boundary condition for the Poisson problem.
Definition: leveque.h:25