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MatrixPartitionedTyings.hpp
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/**
Implementation of MatrixPartitionedTyings.h
\file MatrixPartitionedTyings.hpp
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#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)
{
GOOSEFEM_ASSERT(Cdu.rows() == Cdp.rows());
m_conn = conn;
m_dofs = dofs;
m_Cdu = Cdu;
m_Cdp = Cdp;
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_nnu, m_nnu + m_nnp);
m_iid = xt::arange<size_t>(m_nni, m_nni + m_nnd);
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(m_ndof <= m_nnode * m_ndim);
GOOSEFEM_ASSERT(m_ndof == xt::amax(m_dofs)() + 1);
}
inline size_t MatrixPartitionedTyings::nnu() const
{
return m_nnu;
}
inline size_t MatrixPartitionedTyings::nnp() const
{
return m_nnp;
}
inline size_t MatrixPartitionedTyings::nni() const
{
return m_nni;
}
inline size_t MatrixPartitionedTyings::nnd() const
{
return m_nnd;
}
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::assemble(const xt::xtensor<double, 3>& elemmat)
{
GOOSEFEM_ASSERT(xt::has_shape(elemmat, {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 && 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 && 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 && 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 && 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_changed = true;
}
inline Eigen::VectorXd MatrixPartitionedTyings::AsDofs_u(const xt::xtensor<double, 1>& dofval) const
{
GOOSEFEM_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
{
GOOSEFEM_ASSERT(xt::has_shape(nodevec, {m_nnode, m_ndim}));
Eigen::VectorXd dofval_u = Eigen::VectorXd::Zero(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
{
GOOSEFEM_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
{
GOOSEFEM_ASSERT(xt::has_shape(nodevec, {m_nnode, m_ndim}));
Eigen::VectorXd dofval_p = Eigen::VectorXd::Zero(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 && 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
{
GOOSEFEM_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
{
GOOSEFEM_ASSERT(xt::has_shape(nodevec, {m_nnode, m_ndim}));
Eigen::VectorXd dofval_d = Eigen::VectorXd::Zero(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;
}
template <class Solver>
inline void MatrixPartitionedTyingsSolver<Solver>::factorize(MatrixPartitionedTyings& matrix)
{
if (!matrix.m_changed && !m_factor) {
return;
}
matrix.m_ACuu = matrix.m_Auu + matrix.m_Aud * matrix.m_Cdu + matrix.m_Cud * matrix.m_Adu +
matrix.m_Cud * matrix.m_Add * matrix.m_Cdu;
matrix.m_ACup = matrix.m_Aup + matrix.m_Aud * matrix.m_Cdp + matrix.m_Cud * matrix.m_Adp +
matrix.m_Cud * matrix.m_Add * matrix.m_Cdp;
// matrix.m_ACpu = matrix.m_Apu + matrix.m_Apd * matrix.m_Cdu + matrix.m_Cpd * matrix.m_Adu
// + matrix.m_Cpd * matrix.m_Add * matrix.m_Cdu;
// matrix.m_ACpp = matrix.m_App + matrix.m_Apd * matrix.m_Cdp + matrix.m_Cpd * matrix.m_Adp
// + matrix.m_Cpd * matrix.m_Add * matrix.m_Cdp;
m_solver.compute(matrix.m_ACuu);
m_factor = false;
matrix.m_changed = false;
}
template <class Solver>
inline void MatrixPartitionedTyingsSolver<Solver>::solve(
MatrixPartitionedTyings& matrix, const xt::xtensor<double, 2>& b, xt::xtensor<double, 2>& x)
{
GOOSEFEM_ASSERT(xt::has_shape(b, {matrix.m_nnode, matrix.m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(x, {matrix.m_nnode, matrix.m_ndim}));
this->factorize(matrix);
Eigen::VectorXd B_u = matrix.AsDofs_u(b);
Eigen::VectorXd B_d = matrix.AsDofs_d(b);
Eigen::VectorXd X_p = matrix.AsDofs_p(x);
B_u += matrix.m_Cud * B_d;
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - matrix.m_ACup * X_p));
Eigen::VectorXd X_d = matrix.m_Cdu * X_u + matrix.m_Cdp * X_p;
#pragma omp parallel for
for (size_t m = 0; m < matrix.m_nnode; ++m) {
for (size_t i = 0; i < matrix.m_ndim; ++i) {
if (matrix.m_dofs(m, i) < matrix.m_nnu) {
x(m, i) = X_u(matrix.m_dofs(m, i));
}
else if (matrix.m_dofs(m, i) >= matrix.m_nni) {
x(m, i) = X_d(matrix.m_dofs(m, i) - matrix.m_nni);
}
}
}
}
template <class Solver>
inline void MatrixPartitionedTyingsSolver<Solver>::solve(
MatrixPartitionedTyings& matrix, const xt::xtensor<double, 1>& b, xt::xtensor<double, 1>& x)
{
GOOSEFEM_ASSERT(b.size() == matrix.m_ndof);
GOOSEFEM_ASSERT(x.size() == matrix.m_ndof);
this->factorize(matrix);
Eigen::VectorXd B_u = matrix.AsDofs_u(b);
Eigen::VectorXd B_d = matrix.AsDofs_d(b);
Eigen::VectorXd X_p = matrix.AsDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - matrix.m_ACup * X_p));
Eigen::VectorXd X_d = matrix.m_Cdu * X_u + matrix.m_Cdp * X_p;
#pragma omp parallel for
for (size_t d = 0; d < matrix.m_nnu; ++d) {
x(matrix.m_iiu(d)) = X_u(d);
}
#pragma omp parallel for
for (size_t d = 0; d < matrix.m_nnd; ++d) {
x(matrix.m_iid(d)) = X_d(d);
}
}
template <class Solver>
inline void MatrixPartitionedTyingsSolver<Solver>::solve_u(
MatrixPartitionedTyings& matrix,
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)
{
UNUSED(b_d);
GOOSEFEM_ASSERT(b_u.size() == matrix.m_nnu);
GOOSEFEM_ASSERT(b_d.size() == matrix.m_nnd);
GOOSEFEM_ASSERT(x_p.size() == matrix.m_nnp);
GOOSEFEM_ASSERT(x_u.size() == matrix.m_nnu);
this->factorize(matrix);
Eigen::Map<Eigen::VectorXd>(x_u.data(), x_u.size()).noalias() = m_solver.solve(Eigen::VectorXd(
Eigen::Map<const Eigen::VectorXd>(b_u.data(), b_u.size()) -
matrix.m_ACup * Eigen::Map<const Eigen::VectorXd>(x_p.data(), x_p.size())));
}
template <class Solver>
inline xt::xtensor<double, 2> MatrixPartitionedTyingsSolver<Solver>::Solve(
MatrixPartitionedTyings& matrix,
const xt::xtensor<double, 2>& b,
const xt::xtensor<double, 2>& x)
{
xt::xtensor<double, 2> ret = x;
this->solve(matrix, b, ret);
return ret;
}
template <class Solver>
inline xt::xtensor<double, 1> MatrixPartitionedTyingsSolver<Solver>::Solve(
MatrixPartitionedTyings& matrix,
const xt::xtensor<double, 1>& b,
const xt::xtensor<double, 1>& x)
{
xt::xtensor<double, 1> ret = x;
this->solve(matrix, b, ret);
return ret;
}
template <class Solver>
inline xt::xtensor<double, 1> MatrixPartitionedTyingsSolver<Solver>::Solve_u(
MatrixPartitionedTyings& matrix,
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 = xt::empty<double>({matrix.m_nnu});
this->solve_u(matrix, b_u, b_d, x_p, x_u);
return x_u;
}
} // namespace GooseFEM
#endif

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