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Vector.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_VECTOR_CPP
#define GOOSEFEM_VECTOR_CPP
// -------------------------------------------------------------------------------------------------
#include "Vector.h"
// =========================================== GooseFEM ============================================
namespace GooseFEM {
// ------------------------------------------ constructor ------------------------------------------
inline Vector::Vector(const xt::xtensor<size_t,2> &conn, const xt::xtensor<size_t,2> &dofs) :
m_conn(conn), m_dofs(dofs)
{
// extract mesh dimensions
m_nelem = static_cast<size_t>(m_conn.shape()[0]);
m_nne = static_cast<size_t>(m_conn.shape()[1]);
m_nnode = static_cast<size_t>(m_dofs.shape()[0]);
m_ndim = static_cast<size_t>(m_dofs.shape()[1]);
m_ndof = static_cast<size_t>(xt::amax(m_dofs)[0] + 1);
m_nnp = 0;
m_nnu = m_ndof;
m_iiu = xt::arange<size_t>(m_ndof);
m_iip = xt::empty<size_t>({0});
// check consistency
assert( xt::amax(m_conn)[0] + 1 == m_nnode );
assert( m_ndof <= m_nnode * m_ndim );
}
// ------------------------------------------ constructor ------------------------------------------
inline Vector::Vector(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)
{
// extract mesh dimensions
m_nelem = static_cast<size_t>(m_conn.shape()[0]);
m_nne = static_cast<size_t>(m_conn.shape()[1]);
m_nnode = static_cast<size_t>(m_dofs.shape()[0]);
m_ndim = static_cast<size_t>(m_dofs.shape()[1]);
m_ndof = static_cast<size_t>(xt::amax(m_dofs)[0] + 1);
m_nnp = static_cast<size_t>(m_iip .size());
m_nnu = m_ndof - m_nnp;
// check consistency
assert( xt::amax(m_conn)[0] + 1 == m_nnode );
assert( m_ndof <= m_nnode * m_ndim );
// reorder DOFs such that they can be used for partitioning; renumber such that
// "iiu" -> beginning
// "iip" -> end
// (otherwise preserving the order)
// this array can be used to assemble to/from partitioned arrays
m_part = Mesh::reorder(m_dofs, m_iip, "end");
// extract unknown DOFs
// - allocate
m_iiu = xt::empty<size_t>({m_nnu});
// - set
#pragma omp parallel for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
if ( m_part(n,i) < m_nnu )
m_iiu(m_part(n,i)) = m_dofs(n,i);
}
// -------------------------------------- number of elements ---------------------------------------
inline size_t Vector::nelem() const
{
return m_nelem;
}
// ---------------------------------- number of nodes per element ----------------------------------
inline size_t Vector::nne() const
{
return m_nne;
}
// ---------------------------------------- number of nodes ----------------------------------------
inline size_t Vector::nnode() const
{
return m_nnode;
}
// ------------------------------------- number of dimensions --------------------------------------
inline size_t Vector::ndim() const
{
return m_ndim;
}
// ---------------------------------------- number of DOFs -----------------------------------------
inline size_t Vector::ndof() const
{
return m_ndof;
}
// ------------------------------------ number of unknown DOFs -------------------------------------
inline size_t Vector::nnu() const
{
return m_nnu;
}
// ----------------------------------- number of prescribed DOFs -----------------------------------
inline size_t Vector::nnp() const
{
return m_nnp;
}
// ------------------------------------------ return DOFs ------------------------------------------
inline xt::xtensor<size_t,2> Vector::dofs() const
{
return m_dofs;
}
// -------------------------------------- return unknown DOFs --------------------------------------
inline xt::xtensor<size_t,1> Vector::iiu() const
{
return m_iiu;
}
// ------------------------------------ return prescribed DOFs -------------------------------------
inline xt::xtensor<size_t,1> Vector::iip() const
{
return m_iip;
}
// --------------------------------------- dofval -> dofval ----------------------------------------
inline xt::xtensor<double,1> Vector::asDofs(const xt::xtensor<double,1> &dofval_u, const xt::xtensor<double,1> &dofval_p) const
{
// check input
assert( static_cast<size_t>(dofval_u.size()) == m_nnu );
assert( static_cast<size_t>(dofval_p.size()) == m_nnp );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_ndof});
// apply conversion
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnu ; ++i ) dofval(m_iiu(i)) = dofval_u(i);
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnp ; ++i ) dofval(m_iip(i)) = dofval_p(i);
return dofval;
}
// --------------------------------------- nodevec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::asDofs(const xt::xtensor<double,2> &nodevec) const
{
// check input
assert( static_cast<size_t>(nodevec.shape()[0]) == m_nnode );
assert( static_cast<size_t>(nodevec.shape()[1]) == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_ndof});
// apply conversion
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
dofval(m_dofs(n,i)) = nodevec(n,i);
return dofval;
}
// --------------------------------------- nodevec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::asDofs_u(const xt::xtensor<double,2> &nodevec) const
{
// check input
assert( static_cast<size_t>(nodevec.shape()[0]) == m_nnode );
assert( static_cast<size_t>(nodevec.shape()[1]) == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnu});
// apply conversion
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
if ( m_part(n,i) < m_nnu )
dofval(m_part(n,i)) = nodevec(n,i);
return dofval;
}
// --------------------------------------- nodevec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::asDofs_p(const xt::xtensor<double,2> &nodevec) const
{
// check input
assert( static_cast<size_t>(nodevec.shape()[0]) == m_nnode );
assert( static_cast<size_t>(nodevec.shape()[1]) == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnp});
// apply conversion
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
if ( m_part(n,i) >= m_nnu )
dofval(m_part(n,i)-m_nnu) = nodevec(n,i);
return dofval;
}
// --------------------------------------- elemvec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::asDofs(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_ndof});
// apply conversion
#pragma omp for
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 )
dofval(m_dofs(m_conn(e,m),i)) = elemvec(e,m,i);
return dofval;
}
// --------------------------------------- elemvec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::asDofs_u(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnu});
// apply conversion
#pragma omp for
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 )
if ( m_part(m_conn(e,m),i) < m_nnu )
dofval(m_part(m_conn(e,m),i)) = elemvec(e,m,i);
return dofval;
}
// --------------------------------------- elemvec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::asDofs_p(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnp});
// apply conversion
#pragma omp for
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 )
if ( m_part(m_conn(e,m),i) >= m_nnu )
dofval(m_part(m_conn(e,m),i)-m_nnu) = elemvec(e,m,i);
return dofval;
}
// --------------------------------------- dofval -> nodevec ---------------------------------------
inline xt::xtensor<double,2> Vector::asNode(const xt::xtensor<double,1> &dofval) const
{
// check input
assert( static_cast<size_t>(dofval.size()) == m_ndof );
// zero-initialize output
xt::xtensor<double,2> nodevec = xt::zeros<double>({m_nnode, m_ndim});
// apply conversion
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
nodevec(n,i) = dofval(m_dofs(n,i));
return nodevec;
}
// --------------------------------------- dofval -> nodevec ---------------------------------------
inline xt::xtensor<double,2> Vector::asNode(const xt::xtensor<double,1> &dofval_u, const xt::xtensor<double,1> &dofval_p) const
{
// check input
assert( static_cast<size_t>(dofval_u.size()) == m_nnu );
assert( static_cast<size_t>(dofval_p.size()) == m_nnp );
// zero-initialize output
xt::xtensor<double,2> nodevec = xt::zeros<double>({m_nnode, m_ndim});
// apply conversion
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n ) {
for ( size_t i = 0 ; i < m_ndim ; ++i ) {
if ( m_part(n,i) < m_nnu ) nodevec(n,i) = dofval_u(m_part(n,i) );
else nodevec(n,i) = dofval_p(m_part(n,i)-m_nnu);
}
}
return nodevec;
}
// --------------------------------------- elemvec -> nodevec ---------------------------------------
inline xt::xtensor<double,2> Vector::asNode(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,2> nodevec = xt::zeros<double>({m_nnode, m_ndim});
// apply conversion
#pragma omp for
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 )
nodevec(m_conn(e,m),i) = elemvec(e,m,i);
return nodevec;
}
// --------------------------------------- dofval -> elemvec ---------------------------------------
inline xt::xtensor<double,3> Vector::asElement(const xt::xtensor<double,1> &dofval) const
{
// check input
assert( static_cast<size_t>(dofval.size()) == m_ndof );
// zero-initialize output: nodal vectors stored per element
xt::xtensor<double,3> elemvec = xt::zeros<double>({m_nelem, m_nne, m_ndim});
// read from nodal vectors
#pragma omp parallel for
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 )
elemvec(e,m,i) = dofval(m_dofs(m_conn(e,m),i));
return elemvec;
}
// --------------------------------------- dofval -> elemvec ---------------------------------------
inline xt::xtensor<double,3> Vector::asElement(const xt::xtensor<double,1> &dofval_u, const xt::xtensor<double,1> &dofval_p) const
{
// check input
assert( static_cast<size_t>(dofval_u.size()) == m_nnu );
assert( static_cast<size_t>(dofval_p.size()) == m_nnp );
// zero-initialize output: nodal vectors stored per element
xt::xtensor<double,3> elemvec = xt::zeros<double>({m_nelem, m_nne, m_ndim});
// read from nodal vectors
#pragma omp parallel for
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 ) {
if ( m_part(m_conn(e,m),i)<m_nnu ) elemvec(e,m,i) = dofval_u(m_part(m_conn(e,m),i) );
else elemvec(e,m,i) = dofval_p(m_part(m_conn(e,m),i)-m_nnu);
}
}
}
return elemvec;
}
// -------------------------------------- nodevec -> elemvec ---------------------------------------
inline xt::xtensor<double,3> Vector::asElement(const xt::xtensor<double,2> &nodevec) const
{
// check input
assert( static_cast<size_t>(nodevec.shape()[0]) == m_nnode );
assert( static_cast<size_t>(nodevec.shape()[1]) == m_ndim );
// zero-initialize output: nodal vectors stored per element
xt::xtensor<double,3> elemvec = xt::zeros<double>({m_nelem, m_nne, m_ndim});
// read from nodal vectors
#pragma omp parallel for
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 )
elemvec(e,m,i) = nodevec(m_conn(e,m),i);
return elemvec;
}
// --------------------------------------- nodevec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::assembleDofs(const xt::xtensor<double,2> &nodevec) const
{
// check input
assert( static_cast<size_t>(nodevec.shape()[0]) == m_nnode );
assert( static_cast<size_t>(nodevec.shape()[1]) == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_ndof});
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize output
xt::xtensor<double,1> t_dofval = xt::zeros<double>({m_ndof});
// assemble
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
t_dofval(m_dofs(n,i)) += nodevec(n,i);
// reduce: combine result obtained on the different threads
#pragma omp critical
dofval += t_dofval;
}
return dofval;
}
// --------------------------------------- nodevec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::assembleDofs_u(const xt::xtensor<double,2> &nodevec) const
{
// check input
assert( static_cast<size_t>(nodevec.shape()[0]) == m_nnode );
assert( static_cast<size_t>(nodevec.shape()[1]) == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnu});
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize output
xt::xtensor<double,1> t_dofval = xt::zeros<double>({m_nnu});
// assemble
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
if ( m_part(n,i) < m_nnu )
t_dofval(m_part(n,i)) += nodevec(n,i);
// reduce: combine result obtained on the different threads
#pragma omp critical
dofval += t_dofval;
}
return dofval;
}
// --------------------------------------- nodevec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::assembleDofs_p(const xt::xtensor<double,2> &nodevec) const
{
// check input
assert( static_cast<size_t>(nodevec.shape()[0]) == m_nnode );
assert( static_cast<size_t>(nodevec.shape()[1]) == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnp});
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize output
xt::xtensor<double,1> t_dofval = xt::zeros<double>({m_nnp});
// assemble
#pragma omp for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
if ( m_part(n,i) >= m_nnu )
t_dofval(m_part(n,i)-m_nnu) += nodevec(n,i);
// reduce: combine result obtained on the different threads
#pragma omp critical
dofval += t_dofval;
}
return dofval;
}
// --------------------------------------- elemvec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::assembleDofs(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_ndof});
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize output
xt::xtensor<double,1> t_dofval = xt::zeros<double>({m_ndof});
// assemble
#pragma omp for
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 )
t_dofval(m_dofs(m_conn(e,m),i)) += elemvec(e,m,i);
// reduce: combine result obtained on the different threads
#pragma omp critical
dofval += t_dofval;
}
return dofval;
}
// --------------------------------------- elemvec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::assembleDofs_u(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnu});
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize output
xt::xtensor<double,1> t_dofval = xt::zeros<double>({m_nnu});
// assemble
#pragma omp for
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 )
if ( m_part(m_conn(e,m),i) < m_nnu )
t_dofval(m_dofs(m_conn(e,m),i)) += elemvec(e,m,i);
// reduce: combine result obtained on the different threads
#pragma omp critical
dofval += t_dofval;
}
return dofval;
}
// --------------------------------------- elemvec -> dofval ---------------------------------------
inline xt::xtensor<double,1> Vector::assembleDofs_p(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,1> dofval = xt::zeros<double>({m_nnp});
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize output
xt::xtensor<double,1> t_dofval = xt::zeros<double>({m_nnp});
// assemble
#pragma omp for
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 )
if ( m_part(m_conn(e,m),i) >= m_nnu )
t_dofval(m_dofs(m_conn(e,m),i)-m_nnu) += elemvec(e,m,i);
// reduce: combine result obtained on the different threads
#pragma omp critical
dofval += t_dofval;
}
return dofval;
}
// --------------------------------------- elemvec -> nodevec ---------------------------------------
inline xt::xtensor<double,2> Vector::assembleNode(const xt::xtensor<double,3> &elemvec) const
{
// check input
assert( elemvec.shape()[0] == m_nelem );
assert( elemvec.shape()[1] == m_nne );
assert( elemvec.shape()[2] == m_ndim );
// zero-initialize output
xt::xtensor<double,2> nodevec = xt::zeros<double>({m_nnode, m_ndim});
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize output
xt::xtensor<double,2> t_nodevec = xt::zeros<double>({m_nnode, m_ndim});
// assemble
#pragma omp for
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 )
t_nodevec(m_conn(e,m),i) += elemvec(e,m,i);
// reduce: combine result obtained on the different threads
#pragma omp critical
nodevec += t_nodevec;
}
return nodevec;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif

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