Loading...
Searching...
No Matches
dirichlet_hho.cc
Go to the documentation of this file.
#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "sinusprod_dirichlet.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] : "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))
- on_local_sides(u*dot(A(dim)*grad_h(ws),normal())));
auto et = lazy_integrate (on_local_sides(mu*deltat));
auto es = lazy_integrate (on_local_sides(mu*dot(A(dim)*grad_h(us),normal())));
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;
}
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
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
rheolef::inv
tensor_basic< T > inv(const tensor_basic< T > &a, size_t d)
Definition tensor.cc:219
rheolef::D
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 D(const Expr &expr)
D(uh): see the expression page for the full documentation.
Definition field_expr_terminal.h:988
rheolef::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition space_mult.h:120
rheolef::grad_h
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_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:968
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition field_expr_terminal.h:432
rheolef::on_local_sides
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
Definition field_expr_quadrature.h:323
rheolef::lazy_integrate
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
Definition field_lazy_terminal.h:588
rheolef::h_local
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
Definition field_expr_terminal.h:520
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
Definition vec_expr_v2.h:415
rheolef::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition csr.h:455
std
STL namespace.
d
size_t d
Definition neumann-laplace-lambda.cc:28
rheolef.h
rheolef - reference manual
sinusprod_dirichlet.h
The sinus product function – right-hand-side and boundary condition for the Poisson problem.
A
Definition diffusion_isotropic.h:25
f
Definition cavity_dg.h:29
lambda
Definition yield_slip_circle.h:34
u
Definition leveque.h:25