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rGOOSEFEM/include/GooseFEM/MatrixPartitioned.hpp
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MatrixPartitioned.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_MATRIXPARTITIONED_HPP
#define GOOSEFEM_MATRIXPARTITIONED_HPP
// -------------------------------------------------------------------------------------------------
#include "MatrixPartitioned.h"
#include "Mesh.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline MatrixPartitioned<Solver>::MatrixPartitioned(
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_iip(iip)
{
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_iiu = xt::setdiff1d(dofs, iip);
m_ndof = xt::amax(m_dofs)[0] + 1;
m_nnp = m_iip.size();
m_nnu = m_iiu.size();
m_part = Mesh::Reorder({m_iiu, m_iip}).get(m_dofs);
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_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);
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(xt::amax(m_iip)[0] <= xt::amax(m_dofs)[0]);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nelem() const
{ return m_nelem; }
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nne() const
{ return m_nne; }
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nnode() const
{ return m_nnode; }
template <class Solver>
inline size_t MatrixPartitioned<Solver>::ndim() const
{ return m_ndim; }
template <class Solver>
inline size_t MatrixPartitioned<Solver>::ndof() const
{ return m_ndof; }
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nnu() const
{ return m_nnu; }
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nnp() const
{ return m_nnp; }
template <class Solver>
inline xt::xtensor<size_t,2> MatrixPartitioned<Solver>::dofs() const
{ return m_dofs; }
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitioned<Solver>::iiu() const
{ return m_iiu; }
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitioned<Solver>::iip() const
{ return m_iip; }
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::factorize()
{
if (!m_factor) return;
m_solver.compute(m_Auu);
m_factor = false;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::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();
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_part(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_part(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)
m_Tup.push_back(Eigen::Triplet<double>(di ,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
else if (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
m_Tpp.push_back(Eigen::Triplet<double>(di-m_nnu,dj-m_nnu,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_factor = true;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::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 X_p = this->asDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_Aup * 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_part(m,i) < m_nnu )
x(m,i) = X_u(m_part(m,i));
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::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 X_p = this->asDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_Aup * X_p));
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
x(m_iiu(d)) = X_u(d);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::solve_u(
const xt::xtensor<double,1> &b_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &x_u)
{
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
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 X_p(m_nnp,1);
std::copy(b_u.begin(), b_u.end(), B_u.data());
std::copy(x_p.begin(), x_p.end(), X_p.data());
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_Aup * X_p));
std::copy(X_u.data(), X_u.data()+m_nnu, x_u.begin());
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::reaction(
const xt::xtensor<double,2> &x,
xt::xtensor<double,2> &b) const
{
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd X_u = this->asDofs_u(x);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd B_p = m_Apu * X_u + m_App * 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_part(m,i) >= m_nnu)
b(m,i) = B_p(m_part(m,i)-m_nnu);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::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);
Eigen::VectorXd X_u = this->asDofs_u(x);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
b(m_iip(d)) = B_p(d);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::reaction_p(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &b_p) const
{
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_p.size() == m_nnp);
Eigen::VectorXd X_u(m_nnu,1);
Eigen::VectorXd X_p(m_nnp,1);
std::copy(x_u.begin(), x_u.end(), X_u.data());
std::copy(x_p.begin(), x_p.end(), X_p.data());
Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
std::copy(B_p.data(), B_p.data()+m_nnp, b_p.begin());
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,2> MatrixPartitioned<Solver>::Solve(
const xt::xtensor<double,2> &b,
const xt::xtensor<double,2> &x)
{
xt::xtensor<double,2> out = x;
this->solve(b, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::Solve(
const xt::xtensor<double,1> &b,
const xt::xtensor<double,1> &x)
{
xt::xtensor<double,1> out = x;
this->solve(b, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::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;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,2> MatrixPartitioned<Solver>::Reaction(
const xt::xtensor<double,2> &x,
const xt::xtensor<double,2> &b) const
{
xt::xtensor<double,2> out = b;
this->reaction(x, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::Reaction(
const xt::xtensor<double,1> &x,
const xt::xtensor<double,1> &b) const
{
xt::xtensor<double,1> out = b;
this->reaction(x, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::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;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::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;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::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_part(m,i) < m_nnu)
dofval_u(m_part(m,i)) = nodevec(m,i);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::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;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::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_part(m,i) >= m_nnu)
dofval_p(m_part(m,i)-m_nnu) = nodevec(m,i);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
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