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TyingsPeriodic.hpp
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/**
Implementation of TyingsPeriodic.h
\file TyingsPeriodic.hpp
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_TYINGSPERIODIC_HPP
#define GOOSEFEM_TYINGSPERIODIC_HPP
#include "Mesh.h"
#include "TyingsPeriodic.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
namespace GooseFEM {
namespace Tyings {
inline Periodic::Periodic(
const xt::xtensor<double, 2>& coor,
const xt::xtensor<size_t, 2>& dofs,
const xt::xtensor<size_t, 2>& control,
const xt::xtensor<size_t, 2>& nodal_tyings)
: Periodic(coor, dofs, control, nodal_tyings, xt::empty<size_t>({0}))
{
}
inline Periodic::Periodic(
const xt::xtensor<double, 2>& coor,
const xt::xtensor<size_t, 2>& dofs,
const xt::xtensor<size_t, 2>& control,
const xt::xtensor<size_t, 2>& nodal_tyings,
const xt::xtensor<size_t, 1>& iip)
: m_tyings(nodal_tyings), m_coor(coor)
{
m_ndim = m_coor.shape(1);
m_nties = m_tyings.shape(0);
GOOSEFEM_ASSERT(xt::has_shape(m_tyings, {m_nties, size_t(2)}));
GOOSEFEM_ASSERT(xt::has_shape(control, {m_ndim, m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(dofs, m_coor.shape()));
GOOSEFEM_ASSERT(xt::amax(control)() <= xt::amax(dofs)());
GOOSEFEM_ASSERT(xt::amin(control)() >= xt::amin(dofs)());
GOOSEFEM_ASSERT(xt::amax(iip)() <= xt::amax(dofs)());
GOOSEFEM_ASSERT(xt::amin(iip)() >= xt::amin(dofs)());
GOOSEFEM_ASSERT(xt::amax(nodal_tyings)() < m_coor.shape(0));
xt::xtensor<size_t, 1> dependent = xt::view(m_tyings, xt::all(), 1);
xt::xtensor<size_t, 2> dependent_dofs = xt::view(dofs, xt::keep(dependent), xt::all());
xt::xtensor<size_t, 1> iid = xt::flatten(dependent_dofs);
xt::xtensor<size_t, 1> iii = xt::setdiff1d(dofs, iid);
xt::xtensor<size_t, 1> iiu = xt::setdiff1d(iii, iip);
m_nnu = iiu.size();
m_nnp = iip.size();
m_nni = iii.size();
m_nnd = iid.size();
GooseFEM::Mesh::Reorder reorder({iiu, iip, iid});
m_dofs = reorder.apply(dofs);
m_control = reorder.apply(control);
}
inline xt::xtensor<size_t, 2> Periodic::dofs() const
{
return m_dofs;
}
inline xt::xtensor<size_t, 2> Periodic::control() const
{
return m_control;
}
inline xt::xtensor<size_t, 2> Periodic::nodal_tyings() const
{
return m_tyings;
}
inline size_t Periodic::nnu() const
{
return m_nnu;
}
inline size_t Periodic::nnp() const
{
return m_nnp;
}
inline size_t Periodic::nni() const
{
return m_nni;
}
inline size_t Periodic::nnd() const
{
return m_nnd;
}
inline xt::xtensor<size_t, 1> Periodic::iiu() const
{
return xt::arange<size_t>(m_nnu);
}
inline xt::xtensor<size_t, 1> Periodic::iip() const
{
return xt::arange<size_t>(m_nnp) + m_nnu;
}
inline xt::xtensor<size_t, 1> Periodic::iii() const
{
return xt::arange<size_t>(m_nni);
}
inline xt::xtensor<size_t, 1> Periodic::iid() const
{
return xt::arange<size_t>(m_nni, m_nni + m_nnd);
}
inline Eigen::SparseMatrix<double> Periodic::Cdi() const
{
std::vector<Eigen::Triplet<double>> data;
data.reserve(m_nties * m_ndim * (m_ndim + 1));
for (size_t i = 0; i < m_nties; ++i) {
for (size_t j = 0; j < m_ndim; ++j) {
size_t ni = m_tyings(i, 0);
size_t nd = m_tyings(i, 1);
data.push_back(Eigen::Triplet<double>(i * m_ndim + j, m_dofs(ni, j), +1.0));
for (size_t k = 0; k < m_ndim; ++k) {
data.push_back(Eigen::Triplet<double>(
i * m_ndim + j, m_control(j, k), m_coor(nd, k) - m_coor(ni, k)));
}
}
}
Eigen::SparseMatrix<double> Cdi;
Cdi.resize(m_nnd, m_nni);
Cdi.setFromTriplets(data.begin(), data.end());
return Cdi;
}
inline Eigen::SparseMatrix<double> Periodic::Cdu() const
{
std::vector<Eigen::Triplet<double>> data;
data.reserve(m_nties * m_ndim * (m_ndim + 1));
for (size_t i = 0; i < m_nties; ++i) {
for (size_t j = 0; j < m_ndim; ++j) {
size_t ni = m_tyings(i, 0);
size_t nd = m_tyings(i, 1);
if (m_dofs(ni, j) < m_nnu) {
data.push_back(Eigen::Triplet<double>(i * m_ndim + j, m_dofs(ni, j), +1.0));
}
for (size_t k = 0; k < m_ndim; ++k) {
if (m_control(j, k) < m_nnu) {
data.push_back(Eigen::Triplet<double>(
i * m_ndim + j, m_control(j, k), m_coor(nd, k) - m_coor(ni, k)));
}
}
}
}
Eigen::SparseMatrix<double> Cdu;
Cdu.resize(m_nnd, m_nnu);
Cdu.setFromTriplets(data.begin(), data.end());
return Cdu;
}
inline Eigen::SparseMatrix<double> Periodic::Cdp() const
{
std::vector<Eigen::Triplet<double>> data;
data.reserve(m_nties * m_ndim * (m_ndim + 1));
for (size_t i = 0; i < m_nties; ++i) {
for (size_t j = 0; j < m_ndim; ++j) {
size_t ni = m_tyings(i, 0);
size_t nd = m_tyings(i, 1);
if (m_dofs(ni, j) >= m_nnu) {
data.push_back(Eigen::Triplet<double>(i * m_ndim + j, m_dofs(ni, j) - m_nnu, +1.0));
}
for (size_t k = 0; k < m_ndim; ++k) {
if (m_control(j, k) >= m_nnu) {
data.push_back(Eigen::Triplet<double>(
i * m_ndim + j, m_control(j, k) - m_nnu, m_coor(nd, k) - m_coor(ni, k)));
}
}
}
}
Eigen::SparseMatrix<double> Cdp;
Cdp.resize(m_nnd, m_nnp);
Cdp.setFromTriplets(data.begin(), data.end());
return Cdp;
}
inline Control::Control(const xt::xtensor<double, 2>& coor, const xt::xtensor<size_t, 2>& dofs)
: m_coor(coor), m_dofs(dofs)
{
GOOSEFEM_ASSERT(coor.shape().size() == 2);
GOOSEFEM_ASSERT(coor.shape() == dofs.shape());
size_t nnode = coor.shape(0);
size_t ndim = coor.shape(1);
m_control_dofs = xt::arange<size_t>(ndim * ndim).reshape({ndim, ndim});
m_control_dofs += xt::amax(dofs)() + 1;
m_control_nodes = nnode + xt::arange<size_t>(ndim);
m_coor = xt::concatenate(xt::xtuple(coor, xt::zeros<double>({ndim, ndim})));
m_dofs = xt::concatenate(xt::xtuple(dofs, m_control_dofs));
}
inline xt::xtensor<double, 2> Control::coor() const
{
return m_coor;
}
inline xt::xtensor<size_t, 2> Control::dofs() const
{
return m_dofs;
}
inline xt::xtensor<size_t, 2> Control::controlDofs() const
{
return m_control_dofs;
}
inline xt::xtensor<size_t, 1> Control::controlNodes() const
{
return m_control_nodes;
}
} // namespace Tyings
} // namespace GooseFEM
#endif

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