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MatrixDiagonalPartitioned.hpp
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/**
Implementation of MatrixDiagonalPartitioned.h
\file MatrixDiagonalPartitioned.hpp
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_MATRIXDIAGONALPARTITIONED_HPP
#define GOOSEFEM_MATRIXDIAGONALPARTITIONED_HPP
#include "MatrixDiagonalPartitioned.h"
#include "Mesh.h"
namespace GooseFEM {
inline MatrixDiagonalPartitioned::MatrixDiagonalPartitioned(
const xt::xtensor<size_t, 2>& conn,
const xt::xtensor<size_t, 2>& dofs,
const xt::xtensor<size_t, 1>& iip)
{
m_conn = conn;
m_dofs = dofs;
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_ndof = xt::amax(m_dofs)() + 1;
GOOSEFEM_ASSERT(xt::amax(m_conn)() + 1 <= m_nnode);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
GOOSEFEM_ASSERT(xt::amax(iip)() <= xt::amax(m_dofs)());
m_iip = iip;
m_iiu = xt::setdiff1d(dofs, iip);
m_nnp = m_iip.size();
m_nnu = m_iiu.size();
m_part = Mesh::Reorder({m_iiu, m_iip}).apply(m_dofs);
m_Auu = xt::empty<double>({m_nnu});
m_App = xt::empty<double>({m_nnp});
m_inv_uu = xt::empty<double>({m_nnu});
}
inline size_t MatrixDiagonalPartitioned::nnu() const
{
return m_nnu;
}
inline size_t MatrixDiagonalPartitioned::nnp() const
{
return m_nnp;
}
inline xt::xtensor<size_t, 1> MatrixDiagonalPartitioned::iiu() const
{
return m_iiu;
}
inline xt::xtensor<size_t, 1> MatrixDiagonalPartitioned::iip() const
{
return m_iip;
}
inline void MatrixDiagonalPartitioned::factorize()
{
if (!m_changed) {
return;
}
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
m_inv_uu(d) = 1.0 / m_Auu(d);
}
m_changed = false;
}
inline void MatrixDiagonalPartitioned::assemble(const xt::xtensor<double, 3>& elemmat)
{
GOOSEFEM_ASSERT(xt::has_shape(elemmat, {m_nelem, m_nne * m_ndim, m_nne * m_ndim}));
GOOSEFEM_ASSERT(Element::isDiagonal(elemmat));
m_Auu.fill(0.0);
m_App.fill(0.0);
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 d = m_part(m_conn(e, m), i);
if (d < m_nnu) {
m_Auu(d) += elemmat(e, m * m_ndim + i, m * m_ndim + i);
}
else {
m_App(d - m_nnu) += elemmat(e, m * m_ndim + i, m * m_ndim + i);
}
}
}
}
m_changed = true;
}
inline void MatrixDiagonalPartitioned::set(const xt::xtensor<double, 1>& A)
{
GOOSEFEM_ASSERT(A.size() == m_ndof);
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
m_Auu(d) = A(m_iiu(d));
}
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
m_App(d) = A(m_iip(d));
}
m_changed = true;
}
inline void
MatrixDiagonalPartitioned::dot(const xt::xtensor<double, 2>& x, xt::xtensor<double, 2>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, {m_nnode, m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(b, {m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
size_t d = m_part(m, i);
if (d < m_nnu) {
b(m, i) = m_Auu(d) * x(m, i);
}
else {
b(m, i) = m_App(d - m_nnu) * x(m, i);
}
}
}
}
inline void
MatrixDiagonalPartitioned::dot(const xt::xtensor<double, 1>& x, xt::xtensor<double, 1>& b) const
{
GOOSEFEM_ASSERT(x.size() == m_ndof);
GOOSEFEM_ASSERT(b.size() == m_ndof);
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
b(m_iiu(d)) = m_Auu(d) * x(m_iiu(d));
}
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
b(m_iip(d)) = m_App(d) * x(m_iip(d));
}
}
inline void MatrixDiagonalPartitioned::dot_u(
const xt::xtensor<double, 1>& x_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& b_u) const
{
UNUSED(x_p);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
b_u(d) = m_Auu(d) * x_u(d);
}
}
inline void MatrixDiagonalPartitioned::dot_p(
const xt::xtensor<double, 1>& x_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& b_p) const
{
UNUSED(x_u);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_p.size() == m_nnp);
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
b_p(d) = m_App(d) * x_p(d);
}
}
inline void
MatrixDiagonalPartitioned::solve(const xt::xtensor<double, 2>& b, xt::xtensor<double, 2>& x)
{
GOOSEFEM_ASSERT(xt::has_shape(b, {m_nnode, m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(x, {m_nnode, m_ndim}));
this->factorize();
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
if (m_part(m, i) < m_nnu) {
x(m, i) = m_inv_uu(m_part(m, i)) * b(m, i);
}
}
}
}
inline void
MatrixDiagonalPartitioned::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();
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
x(m_iiu(d)) = m_inv_uu(d) * b(m_iiu(d));
}
}
inline void MatrixDiagonalPartitioned::solve_u(
const xt::xtensor<double, 1>& b_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& x_u)
{
UNUSED(x_p);
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
this->factorize();
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
x_u(d) = m_inv_uu(d) * b_u(d);
}
}
inline void MatrixDiagonalPartitioned::reaction(
const xt::xtensor<double, 2>& x, xt::xtensor<double, 2>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, {m_nnode, m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(b, {m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
if (m_part(m, i) >= m_nnu) {
b(m, i) = m_App(m_part(m, i) - m_nnu) * x(m, i);
}
}
}
}
inline void MatrixDiagonalPartitioned::reaction(
const xt::xtensor<double, 1>& x, xt::xtensor<double, 1>& b) const
{
GOOSEFEM_ASSERT(x.size() == m_ndof);
GOOSEFEM_ASSERT(b.size() == m_ndof);
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
b(m_iip(d)) = m_App(d) * x(m_iip(d));
}
}
inline void MatrixDiagonalPartitioned::reaction_p(
const xt::xtensor<double, 1>& x_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& b_p) const
{
UNUSED(x_u);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_p.size() == m_nnp);
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
b_p(d) = m_App(d) * x_p(d);
}
}
inline xt::xtensor<double, 1> MatrixDiagonalPartitioned::Todiagonal() const
{
xt::xtensor<double, 1> ret = xt::zeros<double>({m_ndof});
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
ret(m_iiu(d)) = m_Auu(d);
}
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
ret(m_iip(d)) = m_App(d);
}
return ret;
}
inline xt::xtensor<double, 1> MatrixDiagonalPartitioned::Dot_u(
const xt::xtensor<double, 1>& x_u, const xt::xtensor<double, 1>& x_p) const
{
xt::xtensor<double, 1> b_u = xt::empty<double>({m_nnu});
this->dot_u(x_u, x_p, b_u);
return b_u;
}
inline xt::xtensor<double, 1> MatrixDiagonalPartitioned::Dot_p(
const xt::xtensor<double, 1>& x_u, const xt::xtensor<double, 1>& x_p) const
{
xt::xtensor<double, 1> b_p = xt::empty<double>({m_nnp});
this->dot_p(x_u, x_p, b_p);
return b_p;
}
inline xt::xtensor<double, 1> MatrixDiagonalPartitioned::Solve_u(
const xt::xtensor<double, 1>& b_u, const xt::xtensor<double, 1>& x_p)
{
xt::xtensor<double, 1> x_u = xt::empty<double>({m_nnu});
this->solve_u(b_u, x_p, x_u);
return x_u;
}
inline xt::xtensor<double, 2> MatrixDiagonalPartitioned::Reaction(
const xt::xtensor<double, 2>& x, const xt::xtensor<double, 2>& b) const
{
xt::xtensor<double, 2> ret = b;
this->reaction(x, ret);
return ret;
}
inline xt::xtensor<double, 1> MatrixDiagonalPartitioned::Reaction(
const xt::xtensor<double, 1>& x, const xt::xtensor<double, 1>& b) const
{
xt::xtensor<double, 1> ret = b;
this->reaction(x, ret);
return ret;
}
inline xt::xtensor<double, 1> MatrixDiagonalPartitioned::Reaction_p(
const xt::xtensor<double, 1>& x_u, const xt::xtensor<double, 1>& x_p) const
{
xt::xtensor<double, 1> b_p = xt::empty<double>({m_nnp});
this->reaction_p(x_u, x_p, b_p);
return b_p;
}
} // namespace GooseFEM
#endif

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