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fe_xyz.C
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fe_xyz.C
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// The libMesh Finite Element Library.
// Copyright (C) 2002-2014 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
// Local includes
#include "libmesh/libmesh_logging.h"
#include "libmesh/fe.h"
#include "libmesh/elem.h"
#include "libmesh/fe_interface.h"
namespace libMesh
{
// ------------------------------------------------------------
// XYZ-specific implementations
// Anonymous namespace for local helper functions
namespace {
void xyz_nodal_soln(const Elem* elem,
const Order order,
const std::vector<Number>& elem_soln,
std::vector<Number>& nodal_soln,
unsigned Dim)
{
const unsigned int n_nodes = elem->n_nodes();
const ElemType elem_type = elem->type();
nodal_soln.resize(n_nodes);
const Order totalorder = static_cast<Order>(order + elem->p_level());
switch (totalorder)
{
// Constant shape functions
case CONSTANT:
{
libmesh_assert_equal_to (elem_soln.size(), 1);
const Number val = elem_soln[0];
for (unsigned int n=0; n<n_nodes; n++)
nodal_soln[n] = val;
return;
}
// For other orders do interpolation at the nodes
// explicitly.
default:
{
// FEType object to be passed to various FEInterface functions below.
FEType fe_type(totalorder, XYZ);
const unsigned int n_sf =
// FE<Dim,T>::n_shape_functions(elem_type, totalorder);
FEInterface::n_shape_functions(Dim, fe_type, elem_type);
for (unsigned int n=0; n<n_nodes; n++)
{
libmesh_assert_equal_to (elem_soln.size(), n_sf);
// Zero before summation
nodal_soln[n] = 0;
// u_i = Sum (alpha_i phi_i)
for (unsigned int i=0; i<n_sf; i++)
nodal_soln[n] += elem_soln[i] *
// FE<Dim,T>::shape(elem, order, i, elem->point(n));
FEInterface::shape(Dim, fe_type, elem, i, elem->point(n));
}
return;
} // default
} // switch
} // xyz_nodal_soln()
unsigned int xyz_n_dofs(const ElemType t, const Order o)
{
switch (o)
{
// constant shape functions
// no matter what shape there is only one DOF.
case CONSTANT:
return 1;
// Discontinuous linear shape functions
// expressed in the XYZ monomials.
case FIRST:
{
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
case EDGE4:
return 2;
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 3;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 4;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
// Discontinuous quadratic shape functions
// expressed in the XYZ monomials.
case SECOND:
{
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
case EDGE4:
return 3;
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 6;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 10;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
// Discontinuous cubic shape functions
// expressed in the XYZ monomials.
case THIRD:
{
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
case EDGE4:
return 4;
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 10;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 20;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
// Discontinuous quartic shape functions
// expressed in the XYZ monomials.
case FOURTH:
{
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
return 5;
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 15;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 35;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
default:
{
const unsigned int order = static_cast<unsigned int>(o);
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
return (order+1);
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return (order+1)*(order+2)/2;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return (order+1)*(order+2)*(order+3)/6;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
}
libmesh_error();
return 0;
}
unsigned int xyz_n_dofs_per_elem(const ElemType t,
const Order o)
{
switch (o)
{
// constant shape functions always have 1 DOF per element
case CONSTANT:
return 1;
// Discontinuous linear shape functions
// expressed in the XYZ monomials.
case FIRST:
{
switch (t)
{
case NODEELEM:
return 1;
// 1D linears have 2 DOFs per element
case EDGE2:
case EDGE3:
case EDGE4:
return 2;
// 2D linears have 3 DOFs per element
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 3;
// 3D linears have 4 DOFs per element
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 4;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
// Discontinuous quadratic shape functions
// expressed in the XYZ monomials.
case SECOND:
{
switch (t)
{
case NODEELEM:
return 1;
// 1D quadratics have 3 DOFs per element
case EDGE2:
case EDGE3:
case EDGE4:
return 3;
// 2D quadratics have 6 DOFs per element
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 6;
// 3D quadratics have 10 DOFs per element
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 10;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
// Discontinuous cubic shape functions
// expressed in the XYZ monomials.
case THIRD:
{
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
case EDGE4:
return 4;
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 10;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 20;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
// Discontinuous quartic shape functions
// expressed in the XYZ monomials.
case FOURTH:
{
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
case EDGE4:
return 5;
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return 15;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return 35;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
default:
{
const unsigned int order = static_cast<unsigned int>(o);
switch (t)
{
case NODEELEM:
return 1;
case EDGE2:
case EDGE3:
return (order+1);
case TRI3:
case TRI6:
case QUAD4:
case QUAD8:
case QUAD9:
return (order+1)*(order+2)/2;
case TET4:
case TET10:
case HEX8:
case HEX20:
case HEX27:
case PRISM6:
case PRISM15:
case PRISM18:
case PYRAMID5:
case PYRAMID13:
case PYRAMID14:
return (order+1)*(order+2)*(order+3)/6;
default:
{
#ifdef DEBUG
libMesh::err << "ERROR: Bad ElemType = " << t
<< " for " << o << "th order approximation!"
<< std::endl;
#endif
libmesh_error();
}
}
}
return 0;
}
}
} // anonymous namespace
template <unsigned int Dim>
void FEXYZ<Dim>::init_shape_functions(const std::vector<Point>& qp,
const Elem* elem)
{
libmesh_assert(elem);
this->calculations_started = true;
// If the user forgot to request anything, we'll be safe and
// calculate everything:
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (!this->calculate_phi && !this->calculate_dphi && !this->calculate_d2phi)
this->calculate_phi = this->calculate_dphi = this->calculate_d2phi = true;
#else
if (!this->calculate_phi && !this->calculate_dphi)
this->calculate_phi = this->calculate_dphi = true;
#endif // LIBMESH_ENABLE_SECOND_DERIVATIVES
// Start logging the shape function initialization
START_LOG("init_shape_functions()", "FE");
// The number of quadrature points.
const std::size_t n_qp = qp.size();
// Number of shape functions in the finite element approximation
// space.
const unsigned int n_approx_shape_functions =
this->n_shape_functions(this->get_type(),
this->get_order());
// resize the vectors to hold current data
// Phi are the shape functions used for the FE approximation
{
// (note: GCC 3.4.0 requires the use of this-> here)
if (this->calculate_phi)
this->phi.resize (n_approx_shape_functions);
if (this->calculate_dphi)
{
this->dphi.resize (n_approx_shape_functions);
this->dphidx.resize (n_approx_shape_functions);
this->dphidy.resize (n_approx_shape_functions);
this->dphidz.resize (n_approx_shape_functions);
}
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (this->calculate_d2phi)
{
this->d2phi.resize (n_approx_shape_functions);
this->d2phidx2.resize (n_approx_shape_functions);
this->d2phidxdy.resize (n_approx_shape_functions);
this->d2phidxdz.resize (n_approx_shape_functions);
this->d2phidy2.resize (n_approx_shape_functions);
this->d2phidydz.resize (n_approx_shape_functions);
this->d2phidz2.resize (n_approx_shape_functions);
this->d2phidxi2.resize (n_approx_shape_functions);
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
for (unsigned int i=0; i<n_approx_shape_functions; i++)
{
if (this->calculate_phi)
this->phi[i].resize (n_qp);
if (this->calculate_dphi)
{
this->dphi[i].resize (n_qp);
this->dphidx[i].resize (n_qp);
this->dphidy[i].resize (n_qp);
this->dphidz[i].resize (n_qp);
}
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (this->calculate_d2phi)
{
this->d2phi[i].resize (n_qp);
this->d2phidx2[i].resize (n_qp);
this->d2phidxdy[i].resize (n_qp);
this->d2phidxdz[i].resize (n_qp);
this->d2phidy2[i].resize (n_qp);
this->d2phidydz[i].resize (n_qp);
this->d2phidz2[i].resize (n_qp);
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
}
}
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
//------------------------------------------------------------
// Initialize the data fields, which should only be used for infinite
// elements, to some sensible values, so that using a FE with the
// variational formulation of an InfFE, correct element matrices are
// returned
{
this->weight.resize (n_qp);
this->dweight.resize (n_qp);
this->dphase.resize (n_qp);
for (unsigned int p=0; p<n_qp; p++)
{
this->weight[p] = 1.;
this->dweight[p].zero();
this->dphase[p].zero();
}
}
#endif // ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
// Stop logging the shape function initialization
STOP_LOG("init_shape_functions()", "FE");
}
template <unsigned int Dim>
void FEXYZ<Dim>::compute_shape_functions (const Elem* elem, const std::vector<Point>&)
{
libmesh_assert(elem);
//-------------------------------------------------------------------------
// Compute the shape function values (and derivatives)
// at the Quadrature points. Note that the actual values
// have already been computed via init_shape_functions
// Start logging the shape function computation
START_LOG("compute_shape_functions()", "FE");
const std::vector<Point>& xyz_qp = this->get_xyz();
// Compute the value of the derivative shape function i at quadrature point p
switch (this->dim)
{
case 1:
{
if (this->calculate_phi)
for (unsigned int i=0; i<this->phi.size(); i++)
for (unsigned int p=0; p<this->phi[i].size(); p++)
this->phi[i][p] = FE<Dim,XYZ>::shape (elem, this->fe_type.order, i, xyz_qp[p]);
if (this->calculate_dphi)
for (unsigned int i=0; i<this->dphi.size(); i++)
for (unsigned int p=0; p<this->dphi[i].size(); p++)
{
this->dphi[i][p](0) =
this->dphidx[i][p] = FE<Dim,XYZ>::shape_deriv (elem, this->fe_type.order, i, 0, xyz_qp[p]);
this->dphi[i][p](1) = this->dphidy[i][p] = 0.;
this->dphi[i][p](2) = this->dphidz[i][p] = 0.;
}
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (this->calculate_d2phi)
for (unsigned int i=0; i<this->d2phi.size(); i++)
for (unsigned int p=0; p<this->d2phi[i].size(); p++)
{
this->d2phi[i][p](0,0) =
this->d2phidx2[i][p] = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 0, xyz_qp[p]);
#if LIBMESH_DIM>1
this->d2phi[i][p](0,1) = this->d2phidxdy[i][p] =
this->d2phi[i][p](1,0) = 0.;
this->d2phi[i][p](1,1) = this->d2phidy2[i][p] = 0.;
#if LIBMESH_DIM>2
this->d2phi[i][p](0,2) = this->d2phidxdz[i][p] =
this->d2phi[i][p](2,0) = 0.;
this->d2phi[i][p](1,2) = this->d2phidydz[i][p] =
this->d2phi[i][p](2,1) = 0.;
this->d2phi[i][p](2,2) = this->d2phidz2[i][p] = 0.;
#endif
#endif
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
// All done
break;
}
case 2:
{
if (this->calculate_phi)
for (unsigned int i=0; i<this->phi.size(); i++)
for (unsigned int p=0; p<this->phi[i].size(); p++)
this->phi[i][p] = FE<Dim,XYZ>::shape (elem, this->fe_type.order, i, xyz_qp[p]);
if (this->calculate_dphi)
for (unsigned int i=0; i<this->dphi.size(); i++)
for (unsigned int p=0; p<this->dphi[i].size(); p++)
{
this->dphi[i][p](0) =
this->dphidx[i][p] = FE<Dim,XYZ>::shape_deriv (elem, this->fe_type.order, i, 0, xyz_qp[p]);
this->dphi[i][p](1) =
this->dphidy[i][p] = FE<Dim,XYZ>::shape_deriv (elem, this->fe_type.order, i, 1, xyz_qp[p]);
#if LIBMESH_DIM == 3
this->dphi[i][p](2) = // can only assign to the Z component if LIBMESH_DIM==3
#endif
this->dphidz[i][p] = 0.;
}
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (this->calculate_d2phi)
for (unsigned int i=0; i<this->d2phi.size(); i++)
for (unsigned int p=0; p<this->d2phi[i].size(); p++)
{
this->d2phi[i][p](0,0) =
this->d2phidx2[i][p] = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 0, xyz_qp[p]);
this->d2phi[i][p](0,1) = this->d2phidxdy[i][p] =
this->d2phi[i][p](1,0) = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 1, xyz_qp[p]);
this->d2phi[i][p](1,1) =
this->d2phidy2[i][p] = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 2, xyz_qp[p]);
#if LIBMESH_DIM>2
this->d2phi[i][p](0,2) = this->d2phidxdz[i][p] =
this->d2phi[i][p](2,0) = 0.;
this->d2phi[i][p](1,2) = this->d2phidydz[i][p] =
this->d2phi[i][p](2,1) = 0.;
this->d2phi[i][p](2,2) = this->d2phidz2[i][p] = 0.;
#endif
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
// All done
break;
}
case 3:
{
if (this->calculate_phi)
for (unsigned int i=0; i<this->phi.size(); i++)
for (unsigned int p=0; p<this->phi[i].size(); p++)
this->phi[i][p] = FE<Dim,XYZ>::shape (elem, this->fe_type.order, i, xyz_qp[p]);
if (this->calculate_dphi)
for (unsigned int i=0; i<this->dphi.size(); i++)
for (unsigned int p=0; p<this->dphi[i].size(); p++)
{
this->dphi[i][p](0) =
this->dphidx[i][p] = FE<Dim,XYZ>::shape_deriv (elem, this->fe_type.order, i, 0, xyz_qp[p]);
this->dphi[i][p](1) =
this->dphidy[i][p] = FE<Dim,XYZ>::shape_deriv (elem, this->fe_type.order, i, 1, xyz_qp[p]);
this->dphi[i][p](2) =
this->dphidz[i][p] = FE<Dim,XYZ>::shape_deriv (elem, this->fe_type.order, i, 2, xyz_qp[p]);
}
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (this->calculate_d2phi)
for (unsigned int i=0; i<this->d2phi.size(); i++)
for (unsigned int p=0; p<this->d2phi[i].size(); p++)
{
this->d2phi[i][p](0,0) =
this->d2phidx2[i][p] = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 0, xyz_qp[p]);
this->d2phi[i][p](0,1) = this->d2phidxdy[i][p] =
this->d2phi[i][p](1,0) = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 1, xyz_qp[p]);
this->d2phi[i][p](1,1) =
this->d2phidy2[i][p] = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 2, xyz_qp[p]);
this->d2phi[i][p](0,2) = this->d2phidxdz[i][p] =
this->d2phi[i][p](2,0) = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 3, xyz_qp[p]);
this->d2phi[i][p](1,2) = this->d2phidydz[i][p] =
this->d2phi[i][p](2,1) = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 4, xyz_qp[p]);
this->d2phi[i][p](2,2) = this->d2phidz2[i][p] = FE<Dim,XYZ>::shape_second_deriv (elem, this->fe_type.order, i, 5, xyz_qp[p]);
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
// All done
break;
}
default:
{
libmesh_error();
}
}
// Stop logging the shape function computation
STOP_LOG("compute_shape_functions()", "FE");
}
// Do full-specialization for every dimension, instead
// of explicit instantiation at the end of this file.
// This could be macro-ified so that it fits on one line...
template <>
void FE<0,XYZ>::nodal_soln(const Elem* elem,
const Order order,
const std::vector<Number>& elem_soln,
std::vector<Number>& nodal_soln)
{ xyz_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/0); }
template <>
void FE<1,XYZ>::nodal_soln(const Elem* elem,
const Order order,
const std::vector<Number>& elem_soln,
std::vector<Number>& nodal_soln)
{ xyz_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/1); }
template <>
void FE<2,XYZ>::nodal_soln(const Elem* elem,
const Order order,
const std::vector<Number>& elem_soln,
std::vector<Number>& nodal_soln)
{ xyz_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/2); }
template <>
void FE<3,XYZ>::nodal_soln(const Elem* elem,
const Order order,
const std::vector<Number>& elem_soln,
std::vector<Number>& nodal_soln)
{ xyz_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/3); }
// Full specialization of n_dofs() function for every dimension
template <> unsigned int FE<0,XYZ>::n_dofs(const ElemType t, const Order o) { return xyz_n_dofs(t, o); }
template <> unsigned int FE<1,XYZ>::n_dofs(const ElemType t, const Order o) { return xyz_n_dofs(t, o); }
template <> unsigned int FE<2,XYZ>::n_dofs(const ElemType t, const Order o) { return xyz_n_dofs(t, o); }
template <> unsigned int FE<3,XYZ>::n_dofs(const ElemType t, const Order o) { return xyz_n_dofs(t, o); }
// Full specialization of n_dofs_at_node() function for every dimension.
// XYZ FEMs have no dofs at nodes, only element dofs.
template <> unsigned int FE<0,XYZ>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { return 0; }
template <> unsigned int FE<1,XYZ>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { return 0; }
template <> unsigned int FE<2,XYZ>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { return 0; }
template <> unsigned int FE<3,XYZ>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { return 0; }
// Full specialization of n_dofs_per_elem() function for every dimension.
template <> unsigned int FE<0,XYZ>::n_dofs_per_elem(const ElemType t, const Order o) { return xyz_n_dofs_per_elem(t, o); }
template <> unsigned int FE<1,XYZ>::n_dofs_per_elem(const ElemType t, const Order o) { return xyz_n_dofs_per_elem(t, o); }
template <> unsigned int FE<2,XYZ>::n_dofs_per_elem(const ElemType t, const Order o) { return xyz_n_dofs_per_elem(t, o); }
template <> unsigned int FE<3,XYZ>::n_dofs_per_elem(const ElemType t, const Order o) { return xyz_n_dofs_per_elem(t, o); }
// Full specialization of get_continuity() function for every dimension.
template <> FEContinuity FE<0,XYZ>::get_continuity() const { return DISCONTINUOUS; }
template <> FEContinuity FE<1,XYZ>::get_continuity() const { return DISCONTINUOUS; }
template <> FEContinuity FE<2,XYZ>::get_continuity() const { return DISCONTINUOUS; }
template <> FEContinuity FE<3,XYZ>::get_continuity() const { return DISCONTINUOUS; }
// Full specialization of is_hierarchic() function for every dimension.
// The XYZ shape functions are hierarchic!
template <> bool FE<0,XYZ>::is_hierarchic() const { return true; }
template <> bool FE<1,XYZ>::is_hierarchic() const { return true; }
template <> bool FE<2,XYZ>::is_hierarchic() const { return true; }
template <> bool FE<3,XYZ>::is_hierarchic() const { return true; }
#ifdef LIBMESH_ENABLE_AMR
// Full specialization of compute_constraints() function for 2D and
// 3D only. There are no constraints for discontinuous elements, so
// we do nothing.
template <> void FE<2,XYZ>::compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem*) {}
template <> void FE<3,XYZ>::compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem*) {}
#endif // #ifdef LIBMESH_ENABLE_AMR
// Full specialization of shapes_need_reinit() function for every dimension.
template <> bool FE<0,XYZ>::shapes_need_reinit() const { return true; }
template <> bool FE<1,XYZ>::shapes_need_reinit() const { return true; }
template <> bool FE<2,XYZ>::shapes_need_reinit() const { return true; }
template <> bool FE<3,XYZ>::shapes_need_reinit() const { return true; }
// Explicit instantiations for non-static FEXYZ member functions.
// These non-static member functions map more naturally to explicit
// instantiations than the functions above:
//
// 1.) Since they are member functions, they rely on
// private/protected member data, and therefore do not work well
// with the "anonymous function call" model we've used above for
// the specializations.
//
// 2.) There is (IMHO) less chance of the linker calling the
// wrong version of one of these member functions, since there is
// only one FEXYZ.
template void FEXYZ<0>::init_shape_functions(const std::vector<Point>&, const Elem*);
template void FEXYZ<1>::init_shape_functions(const std::vector<Point>&, const Elem*);
template void FEXYZ<2>::init_shape_functions(const std::vector<Point>&, const Elem*);
template void FEXYZ<3>::init_shape_functions(const std::vector<Point>&, const Elem*);
template void FEXYZ<0>::compute_shape_functions(const Elem*,const std::vector<Point>&);
template void FEXYZ<1>::compute_shape_functions(const Elem*,const std::vector<Point>&);
template void FEXYZ<2>::compute_shape_functions(const Elem*,const std::vector<Point>&);
template void FEXYZ<3>::compute_shape_functions(const Elem*,const std::vector<Point>&);
} // namespace libMesh