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MatrixPartitionedTyings.hpp
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MatrixPartitionedTyings.hpp
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXPARTITIONEDTYINGS_HPP
#define GOOSEFEM_MATRIXPARTITIONEDTYINGS_HPP
// -------------------------------------------------------------------------------------------------
#include "MatrixPartitionedTyings.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
inline MatrixPartitionedTyings::MatrixPartitionedTyings(
const xt::xtensor<size_t,2> &conn,
const xt::xtensor<size_t,2> &dofs,
const Eigen::SparseMatrix<double>& Cdu,
const Eigen::SparseMatrix<double>& Cdp) :
m_conn(conn),
m_dofs(dofs),
m_Cdu(Cdu),
m_Cdp(Cdp)
{
GOOSEFEM_ASSERT(Cdu.rows() == Cdp.rows());
m_nnu = static_cast<size_t>(m_Cdu.cols());
m_nnp = static_cast<size_t>(m_Cdp.cols());
m_nnd = static_cast<size_t>(m_Cdp.rows());
m_nni = m_nnu + m_nnp;
m_ndof = m_nni + m_nnd;
m_iiu = xt::arange<size_t>(m_nnu);
m_iip = xt::arange<size_t>(m_nnp) + m_nnu;
m_iid = xt::arange<size_t>(m_nnd) + m_nni;
m_nelem = m_conn.shape()[0];
m_nne = m_conn.shape()[1];
m_nnode = m_dofs.shape()[0];
m_ndim = m_dofs.shape()[1];
m_Cud = m_Cdu.transpose();
m_Cpd = m_Cdp.transpose();
m_Tuu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tup.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tpu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tpp.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tud.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tpd.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tdu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tdp.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tdd.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Auu.resize(m_nnu,m_nnu);
m_Aup.resize(m_nnu,m_nnp);
m_Apu.resize(m_nnp,m_nnu);
m_App.resize(m_nnp,m_nnp);
m_Aud.resize(m_nnu,m_nnd);
m_Apd.resize(m_nnp,m_nnd);
m_Adu.resize(m_nnd,m_nnu);
m_Adp.resize(m_nnd,m_nnp);
m_Add.resize(m_nnd,m_nnd);
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
GOOSEFEM_ASSERT(m_ndof == xt::amax(m_dofs)[0] + 1);
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixPartitionedTyings::nelem() const
{ return m_nelem; }
inline size_t MatrixPartitionedTyings::nne() const
{ return m_nne; }
inline size_t MatrixPartitionedTyings::nnode() const
{ return m_nnode; }
inline size_t MatrixPartitionedTyings::ndim() const
{ return m_ndim; }
inline size_t MatrixPartitionedTyings::ndof() const
{ return m_ndof; }
inline size_t MatrixPartitionedTyings::nnu() const
{ return m_nnu; }
inline size_t MatrixPartitionedTyings::nnp() const
{ return m_nnp; }
inline xt::xtensor<size_t,2> MatrixPartitionedTyings::dofs() const
{ return m_dofs; }
inline xt::xtensor<size_t,1> MatrixPartitionedTyings::iiu() const
{ return m_iiu; }
inline xt::xtensor<size_t,1> MatrixPartitionedTyings::iip() const
{ return m_iip; }
inline xt::xtensor<size_t,1> MatrixPartitionedTyings::iii() const
{ return xt::arange<size_t>(m_nni); }
inline xt::xtensor<size_t,1> MatrixPartitionedTyings::iid() const
{ return m_iid; }
// -------------------------------------------------------------------------------------------------
inline void MatrixPartitionedTyings::factorize()
{
if (!m_factor) return;
m_ACuu = m_Auu + m_Aud * m_Cdu + m_Cud * m_Adu + m_Cud * m_Add * m_Cdu;
m_ACup = m_Aup + m_Aud * m_Cdp + m_Cud * m_Adp + m_Cud * m_Add * m_Cdp;
// m_ACpu = m_Apu + m_Apd * m_Cdu + m_Cpd * m_Adu + m_Cpd * m_Add * m_Cdu;
// m_ACpp = m_App + m_Apd * m_Cdp + m_Cpd * m_Adp + m_Cpd * m_Add * m_Cdp;
m_solver.compute(m_ACuu);
m_factor = false;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixPartitionedTyings::assemble(const xt::xtensor<double,3> &elemmat)
{
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
m_Tuu.clear();
m_Tup.clear();
m_Tpu.clear();
m_Tpp.clear();
m_Tud.clear();
m_Tpd.clear();
m_Tdu.clear();
m_Tdp.clear();
m_Tdd.clear();
for (size_t e = 0 ; e < m_nelem ; ++e) {
for (size_t m = 0 ; m < m_nne ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
size_t di = m_dofs(m_conn(e,m),i);
for (size_t n = 0 ; n < m_nne ; ++n) {
for (size_t j = 0 ; j < m_ndim ; ++j) {
size_t dj = m_dofs(m_conn(e,n),j);
if (di < m_nnu and dj < m_nnu)
m_Tuu.push_back(Eigen::Triplet<double>(di ,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (di < m_nnu and dj < m_nni)
m_Tup.push_back(Eigen::Triplet<double>(di ,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (di < m_nnu)
m_Tud.push_back(Eigen::Triplet<double>(di ,dj-m_nni,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (di < m_nni and dj < m_nnu)
m_Tpu.push_back(Eigen::Triplet<double>(di-m_nnu,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (di < m_nni and dj < m_nni)
m_Tpp.push_back(Eigen::Triplet<double>(di-m_nnu,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (di < m_nni)
m_Tpd.push_back(Eigen::Triplet<double>(di-m_nnu,dj-m_nni,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (dj < m_nnu)
m_Tdu.push_back(Eigen::Triplet<double>(di-m_nni,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (dj < m_nni)
m_Tdp.push_back(Eigen::Triplet<double>(di-m_nni,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else
m_Tdd.push_back(Eigen::Triplet<double>(di-m_nni,dj-m_nni,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
}
}
}
}
}
m_Auu.setFromTriplets(m_Tuu.begin(), m_Tuu.end());
m_Aup.setFromTriplets(m_Tup.begin(), m_Tup.end());
m_Apu.setFromTriplets(m_Tpu.begin(), m_Tpu.end());
m_App.setFromTriplets(m_Tpp.begin(), m_Tpp.end());
m_Aud.setFromTriplets(m_Tud.begin(), m_Tud.end());
m_Apd.setFromTriplets(m_Tpd.begin(), m_Tpd.end());
m_Adu.setFromTriplets(m_Tdu.begin(), m_Tdu.end());
m_Adp.setFromTriplets(m_Tdp.begin(), m_Tdp.end());
m_Add.setFromTriplets(m_Tdd.begin(), m_Tdd.end());
m_factor = true;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixPartitionedTyings::solve(
const xt::xtensor<double,2> &b,
xt::xtensor<double,2> &x)
{
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
this->factorize();
Eigen::VectorXd B_u = this->asDofs_u(b);
Eigen::VectorXd B_d = this->asDofs_d(b);
Eigen::VectorXd X_p = this->asDofs_p(x);
B_u += m_Cud * B_d;
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_ACup * X_p));
Eigen::VectorXd X_d = m_Cdu * X_u + m_Cdp * X_p;
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
if (m_dofs(m,i) < m_nnu)
x(m,i) = X_u(m_dofs(m,i));
else if (m_dofs(m,i) >= m_nni)
x(m,i) = X_d(m_dofs(m,i)-m_nni);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void MatrixPartitionedTyings::solve(
const xt::xtensor<double,1> &b,
xt::xtensor<double,1> &x)
{
GOOSEFEM_ASSERT(b.size() == m_ndof);
GOOSEFEM_ASSERT(x.size() == m_ndof);
this->factorize();
Eigen::VectorXd B_u = this->asDofs_u(b);
Eigen::VectorXd B_d = this->asDofs_d(b);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_ACup * X_p));
Eigen::VectorXd X_d = m_Cdu * X_u + m_Cdp * X_p;
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
x(m_iiu(d)) = X_u(d);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnd ; ++d)
x(m_iid(d)) = X_d(d);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixPartitionedTyings::solve_u(
const xt::xtensor<double,1> &b_u,
const xt::xtensor<double,1> &b_d,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &x_u)
{
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
GOOSEFEM_ASSERT(b_d.size() == m_nnd);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
this->factorize();
Eigen::VectorXd B_u(m_nnu,1);
Eigen::VectorXd B_d(m_nnd,1);
Eigen::VectorXd X_p(m_nnp,1);
std::copy(b_u.begin(), b_u.end(), B_u.data());
std::copy(b_d.begin(), b_d.end(), B_d.data());
std::copy(x_p.begin(), x_p.end(), X_p.data());
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_ACup * X_p));
std::copy(X_u.data(), X_u.data()+m_nnu, x_u.begin());
}
// -------------------------------------------------------------------------------------------------
inline Eigen::VectorXd MatrixPartitionedTyings::asDofs_u(
const xt::xtensor<double,1> &dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_u(m_nnu,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
dofval_u(d) = dofval(m_iiu(d));
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::VectorXd MatrixPartitionedTyings::asDofs_u(
const xt::xtensor<double,2> &nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_u(m_nnu,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_dofs(m,i) < m_nnu)
dofval_u(m_dofs(m,i)) = nodevec(m,i);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::VectorXd MatrixPartitionedTyings::asDofs_p(
const xt::xtensor<double,1> &dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_p(m_nnp,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
dofval_p(d) = dofval(m_iip(d));
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::VectorXd MatrixPartitionedTyings::asDofs_p(
const xt::xtensor<double,2> &nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_p(m_nnp,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_dofs(m,i) >= m_nnu and m_dofs(m,i) < m_nni)
dofval_p(m_dofs(m,i)-m_nnu) = nodevec(m,i);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::VectorXd MatrixPartitionedTyings::asDofs_d(
const xt::xtensor<double,1> &dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_d(m_nnd,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnd ; ++d)
dofval_d(d) = dofval(m_iip(d));
return dofval_d;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::VectorXd MatrixPartitionedTyings::asDofs_d(
const xt::xtensor<double,2> &nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_d(m_nnd,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_dofs(m,i) >= m_nni)
dofval_d(m_dofs(m,i)-m_nni) = nodevec(m,i);
return dofval_d;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif

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