element_type exact_project(const space_ptrtype & Xh, const double & val)
{
ex solution = getSolution(val);
auto mesh = Xh->mesh();
auto gproj = vf::project( _space=Xh, _range=elements( mesh ), _expr=expr(solution,vars) );
return gproj;
}
element_type rhs_project(const space_ptrtype & Xh)
{
ex solution = getRhs();
auto mesh = Xh->mesh();
auto gproj = vf::project( _space=Xh, _range=elements( mesh ), _expr=expr(solution,vars) );
return gproj;
}
double L2_error(const space_ptrtype & Xh, const element_type & T, const double & values) const
{
// replace params by specified values
ex solution = getSolution(values);
auto g = expr(solution,vars);
auto mesh = Xh->mesh();
return math::sqrt( integrate( elements(mesh), Px()*(idv(T) - g)*(idv(T) - g) ).evaluate()(0,0) );
}
element_type grad_exact_project(const space_ptrtype & Xh)
{
ex solution = getSolution();
auto gradg = expr<1,Dim,2>(grad(solution,vars), vars );
auto mesh = Xh->mesh();
auto gproj = vf::project( _space=Xh, _range=elements( mesh ), _expr=expr(gradg,vars) );
return gproj;
}
double H1_error(const space_ptrtype & Xh, const element_type & T, const double & values) const
{
// replace params by specified values
ex solution = getSolution(values);
auto gradg = expr<1,Dim,2>(grad(solution,vars), vars );
auto mesh = Xh->mesh();
double L2error = L2_error(Xh, T, values);
double H1seminorm = math::sqrt( integrate( elements(mesh), Px()*(gradv(T) - gradg)*trans(gradv(T) - gradg) ).evaluate()(0,0) );
return math::sqrt( L2error*L2error + H1seminorm*H1seminorm);
}
PreconditionerAS<space_type,coef_space_type>::PreconditionerAS( std::string t,
space_ptrtype Xh,
coef_space_ptrtype Mh,
BoundaryConditions bcFlags,
std::string const& p,
sparse_matrix_ptrtype Pm,
double k )
:
M_type( AS ),
M_Xh( Xh ),
M_Vh(Xh->template functionSpace<0>() ),
M_Qh(Xh->template functionSpace<1>() ),
M_Mh( Mh ),
M_Vh_indices( M_Vh->nLocalDofWithGhost() ),
M_Qh_indices( M_Qh->nLocalDofWithGhost() ),
M_Qh3_indices( Dim ),
A(backend()->newVector(M_Vh)),
B(backend()->newVector(M_Vh)),
C(backend()->newVector(M_Vh)),
M_r(backend()->newVector(M_Vh)),
M_r_t(backend()->newVector(M_Vh)),
M_uout(backend()->newVector(M_Vh)),
M_diagPm(backend()->newVector(M_Vh)),
//M_t(backend()->newVector(M_Vh)),
U( M_Vh, "U" ),
M_mu(M_Mh, "mu"),
M_er(M_Mh, "er"),
M_bcFlags( bcFlags ),
M_prefix( p ),
M_k(k),
M_g(1.-k*k)
{
tic();
LOG(INFO) << "[PreconditionerAS] setup starts";
this->setMatrix( Pm ); // Needed only if worldComm > 1
// QH3 : Lagrange vectorial space type
M_Qh3 = lag_v_space_type::New(Xh->mesh());
M_qh3_elt = M_Qh3->element();
M_qh_elt = M_Qh->element();
M_vh_elt = M_Vh->element();
// Block 11.1
M_s = backend()->newVector(M_Qh3);
M_y = backend()->newVector(M_Qh3);
// Block 11.2
M_z = backend()->newVector(M_Qh);
M_t = backend()->newVector(M_Qh);
// Create the interpolation and keep only the matrix
auto pi_curl = I(_domainSpace=M_Qh3, _imageSpace=M_Vh);
auto Igrad = Grad( _domainSpace=M_Qh, _imageSpace=M_Vh);
M_P = pi_curl.matPtr();
M_C = Igrad.matPtr();
M_Pt = backend()->newMatrix(M_Qh3,M_Vh);
M_Ct = backend()->newMatrix(M_Qh3,M_Vh);
M_P->transpose(M_Pt,MATRIX_TRANSPOSE_UNASSEMBLED);
M_C->transpose(M_Ct,MATRIX_TRANSPOSE_UNASSEMBLED);
LOG(INFO) << "size of M_C = " << M_C->size1() << ", " << M_C->size2() << std::endl;
LOG(INFO) << "size of M_P = " << M_P->size1() << ", " << M_P->size2() << std::endl;
// Create vector of indices to create subvectors/matrices
std::iota( M_Vh_indices.begin(), M_Vh_indices.end(), 0 ); // Vh indices in Xh
std::iota( M_Qh_indices.begin(), M_Qh_indices.end(), M_Vh->nLocalDofWithGhost() ); // Qh indices in Xh
// "Components" of Qh3
auto Qh3_dof_begin = M_Qh3->dof()->dofPointBegin();
auto Qh3_dof_end = M_Qh3->dof()->dofPointEnd();
int dof_comp, dof_idx;
for( auto it = Qh3_dof_begin; it!= Qh3_dof_end; it++ )
{
dof_comp = it->template get<2>(); //Component
dof_idx = it->template get<1>(); //Global index
M_Qh3_indices[dof_comp].push_back( dof_idx );
}
// Subvectors for M_y (per component)
M_y1 = M_y->createSubVector(M_Qh3_indices[0], true);
M_y2 = M_y->createSubVector(M_Qh3_indices[1], true);
#if FEELPP_DIM == 3
M_y3 = M_y->createSubVector(M_Qh3_indices[2], true);
#endif
// Subvectors for M_s (per component)
M_s1 = M_y->createSubVector(M_Qh3_indices[0], true);
M_s2 = M_y->createSubVector(M_Qh3_indices[1], true);
#if FEELPP_DIM == 3
M_s3 = M_y->createSubVector(M_Qh3_indices[2], true);
#endif
this->setType ( t );
toc( "[PreconditionerAS] setup done ", FLAGS_v > 0 );
}