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// The libMesh Finite Element Library.
// Copyright (C) 2002-2008 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
#ifndef __fe_base_h__
#define __fe_base_h__
// C++ includes
#include <vector>
// Local includes
#include "reference_counted_object.h"
#include "point.h"
#include "vector_value.h"
#include "enum_elem_type.h"
#include "fe_type.h"
#include "auto_ptr.h"
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
#include "tensor_value.h"
#endif
namespace libMesh
{
// forward declarations
template <typename T> class DenseMatrix;
template <typename T> class DenseVector;
class BoundaryInfo;
class DofConstraints;
class DofMap;
class Elem;
class MeshBase;
template <typename T> class NumericVector;
class QBase;
#ifdef LIBMESH_ENABLE_PERIODIC
class PeriodicBoundaries;
class PointLocatorBase;
#endif
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
template <unsigned int Dim, FEFamily T_radial, InfMapType T_map>
class InfFE;
#endif
/**
* This class forms the foundation from which generic finite
* elements may be derived. In the current implementation the
* templated derived class \p FE offers a wide variety of commonly
* used finite element concepts. Check there for details.
* Use the \p FEBase::build() method to create an object of any of
* the derived classes.
* Note that the amount of virtual members is kept to a minimum,
* and the sophisticated template scheme of \p FE is quite
* likely to offer acceptably fast code.
*
* All calls to static members of the \p FE classes should be
* requested through the \p FEInterface. This interface class
* offers sort-of runtime polymorphism for the templated finite
* element classes. Even internal library classes, like \p DofMap,
* request the number of dof's through this interface class.
* Note that this also enables the co-existence of various
* element-based schemes.
* This class is well 'at the heart' of the library, so
* things in here should better remain unchanged.
*
* @author Benjamin S. Kirk, 2002
*/
// ------------------------------------------------------------
// FEBase class definition
class FEBase : public ReferenceCountedObject<FEBase>
{
protected:
/**
* Constructor. Optionally initializes required data
* structures. Protected so that this base class
* cannot be explicitly instantiated.
*/
FEBase (const unsigned int dim,
const FEType& fet);
public:
/**
* Destructor.
*/
virtual ~FEBase();
/**
* Builds a specific finite element type. A \p AutoPtr<FEBase> is
* returned to prevent a memory leak. This way the user need not
* remember to delete the object.
*/
static AutoPtr<FEBase> build (const unsigned int dim,
const FEType& type);
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
/**
* Builds a specific infinite element type. A \p AutoPtr<FEBase> is
* returned to prevent a memory leak. This way the user need not
* remember to delete the object.
*/
static AutoPtr<FEBase> build_InfFE (const unsigned int dim,
const FEType& type);
#endif
/**
* This is at the core of this class. Use this for each
* new element in the mesh. Reinitializes the requested physical
* element-dependent data based on the current element
* \p elem. By default the element data computed at the quadrature
* points specified by the quadrature rule \p qrule, but any set
* of points on the reference element may be specified in the optional
* argument \p pts.
*
* Note that the FE classes decide which data to initialize based on
* which accessor functions such as \p get_phi() or \p get_d2phi() have
* been called, so all such accessors should be called before the first
* \p reinit().
*/
virtual void reinit (const Elem* elem,
const std::vector<Point>* const pts = NULL) = 0;
/**
* Reinitializes all the physical element-dependent data based on
* the \p side of the element \p elem. The \p tolerance paremeter
* is passed to the involved call to \p inverse_map().
*/
virtual void reinit (const Elem* elem,
const unsigned int side,
const Real tolerance = TOLERANCE) = 0;
/**
* Reinitializes all the physical element-dependent data based on
* the \p edge of the element \p elem. The \p tolerance paremeter
* is passed to the involved call to \p inverse_map().
*/
virtual void edge_reinit (const Elem* elem,
const unsigned int edge,
const Real tolerance = TOLERANCE) = 0;
/**
* @returns true if the point p is located on the reference element
* for element type t, false otherwise. Since we are doing floating
* point comparisons here the parameter \p eps can be specified to
* indicate a tolerance. For example, \f$ x \le 1 \f$ becomes
* \f$ x \le 1 + \epsilon \f$.
*/
static bool on_reference_element(const Point& p,
const ElemType t,
const Real eps = TOLERANCE);
#ifdef LIBMESH_ENABLE_AMR
/**
* Computes the constraint matrix contributions (for
* non-conforming adapted meshes) corresponding to
* variable number \p var_number, using generic
* projections.
*/
static void compute_proj_constraints (DofConstraints &constraints,
DofMap &dof_map,
const unsigned int variable_number,
const Elem* elem);
/**
* Creates a local projection on \p coarse_elem, based on the
* DoF values in \p global_vector for it's children.
*/
static void coarsened_dof_values(const NumericVector<Number> &global_vector,
const DofMap &dof_map,
const Elem *coarse_elem,
DenseVector<Number> &coarse_dofs,
const unsigned int var,
const bool use_old_dof_indices = false);
#endif // #ifdef LIBMESH_ENABLE_AMR
#ifdef LIBMESH_ENABLE_PERIODIC
/**
* Computes the constraint matrix contributions (for
* meshes with periodic boundary conditions) corresponding to
* variable number \p var_number, using generic projections.
*/
static void compute_periodic_constraints (DofConstraints &constraints,
DofMap &dof_map,
const PeriodicBoundaries &boundaries,
const MeshBase& mesh,
const PointLocatorBase* point_locator,
const unsigned int variable_number,
const Elem* elem);
#endif // LIBMESH_ENABLE_PERIODIC
/**
* @returns the \p xyz spatial locations of the quadrature
* points on the element.
*/
const std::vector<Point>& get_xyz() const
{ return xyz; }
/**
* @returns the shape function values at the quadrature points
* on the element.
*/
const std::vector<std::vector<Real> >& get_phi() const
{ libmesh_assert(!calculations_started || calculate_phi);
calculate_phi = true; return phi; }
/**
* @returns the element Jacobian times the quadrature weight for
* each quadrature point.
*/
const std::vector<Real>& get_JxW() const
{ return JxW; }
/**
* @returns the shape function derivatives at the quadrature
* points.
*/
const std::vector<std::vector<RealGradient> >& get_dphi() const
{ libmesh_assert(!calculations_started || calculate_dphi);
calculate_dphi = true; return dphi; }
/**
* @returns the shape function x-derivative at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_dphidx() const
{ libmesh_assert(!calculations_started || calculate_dphi);
calculate_dphi = true; return dphidx; }
/**
* @returns the shape function y-derivative at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_dphidy() const
{ libmesh_assert(!calculations_started || calculate_dphi);
calculate_dphi = true; return dphidy; }
/**
* @returns the shape function z-derivative at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_dphidz() const
{ libmesh_assert(!calculations_started || calculate_dphi);
calculate_dphi = true; return dphidz; }
/**
* @returns the shape function xi-derivative at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_dphidxi() const
{ libmesh_assert(!calculations_started || calculate_dphi);
calculate_dphi = true; return dphidxi; }
/**
* @returns the shape function eta-derivative at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_dphideta() const
{ libmesh_assert(!calculations_started || calculate_dphi);
calculate_dphi = true; return dphideta; }
/**
* @returns the shape function zeta-derivative at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_dphidzeta() const
{ libmesh_assert(!calculations_started || calculate_dphi);
calculate_dphi = true; return dphidzeta; }
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
/**
* @returns the shape function second derivatives at the quadrature
* points.
*/
const std::vector<std::vector<RealTensor> >& get_d2phi() const
{ libmesh_assert(!calculations_started || calculate_d2phi);
calculate_d2phi = true; return d2phi; }
/**
* @returns the shape function second derivatives at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_d2phidx2() const
{ libmesh_assert(!calculations_started || calculate_d2phi);
calculate_d2phi = true; return d2phidx2; }
/**
* @returns the shape function second derivatives at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_d2phidxdy() const
{ libmesh_assert(!calculations_started || calculate_d2phi);
calculate_d2phi = true; return d2phidxdy; }
/**
* @returns the shape function second derivatives at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_d2phidxdz() const
{ libmesh_assert(!calculations_started || calculate_d2phi);
calculate_d2phi = true; return d2phidxdz; }
/**
* @returns the shape function second derivatives at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_d2phidy2() const
{ libmesh_assert(!calculations_started || calculate_d2phi);
calculate_d2phi = true; return d2phidy2; }
/**
* @returns the shape function second derivatives at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_d2phidydz() const
{ libmesh_assert(!calculations_started || calculate_d2phi);
calculate_d2phi = true; return d2phidydz; }
/**
* @returns the shape function second derivatives at the quadrature
* points.
*/
const std::vector<std::vector<Real> >& get_d2phidz2() const
{ libmesh_assert(!calculations_started || calculate_d2phi);
calculate_d2phi = true; return d2phidz2; }
#endif
/**
* @returns the element tangents in xi-direction at the quadrature
* points.
*/
const std::vector<RealGradient>& get_dxyzdxi() const
{ return dxyzdxi_map; }
/**
* @returns the element tangents in eta-direction at the quadrature
* points.
*/
const std::vector<RealGradient>& get_dxyzdeta() const
{ return dxyzdeta_map; }
/**
* @returns the element tangents in zeta-direction at the quadrature
* points.
*/
const std::vector<RealGradient>& get_dxyzdzeta() const
{ return dxyzdzeta_map; }
/**
* @returns the second partial derivatives in xi.
*/
const std::vector<RealGradient>& get_d2xyzdxi2() const
{ return d2xyzdxi2_map; }
/**
* @returns the second partial derivatives in eta.
*/
const std::vector<RealGradient>& get_d2xyzdeta2() const
{ return d2xyzdeta2_map; }
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
/**
* @returns the second partial derivatives in zeta.
*/
const std::vector<RealGradient>& get_d2xyzdzeta2() const
{ return d2xyzdzeta2_map; }
#endif
/**
* @returns the second partial derivatives in xi-eta.
*/
const std::vector<RealGradient>& get_d2xyzdxideta() const
{ return d2xyzdxideta_map; }
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
/**
* @returns the second partial derivatives in xi-zeta.
*/
const std::vector<RealGradient>& get_d2xyzdxidzeta() const
{ return d2xyzdxidzeta_map; }
/**
* @returns the second partial derivatives in eta-zeta.
*/
const std::vector<RealGradient>& get_d2xyzdetadzeta() const
{ return d2xyzdetadzeta_map; }
#endif
/**
* @returns the dxi/dx entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_dxidx() const
{ return dxidx_map; }
/**
* @returns the dxi/dy entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_dxidy() const
{ return dxidy_map; }
/**
* @returns the dxi/dz entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_dxidz() const
{ return dxidz_map; }
/**
* @returns the deta/dx entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_detadx() const
{ return detadx_map; }
/**
* @returns the deta/dy entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_detady() const
{ return detady_map; }
/**
* @returns the deta/dz entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_detadz() const
{ return detadz_map; }
/**
* @returns the dzeta/dx entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_dzetadx() const
{ return dzetadx_map; }
/**
* @returns the dzeta/dy entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_dzetady() const
{ return dzetady_map; }
/**
* @returns the dzeta/dz entry in the transformation
* matrix from physical to local coordinates.
*/
const std::vector<Real>& get_dzetadz() const
{ return dzetadz_map; }
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
/**
* @returns the global first derivative of the phase term
* which is used in infinite elements, evaluated at the
* quadrature points.
*
* In case of the general finite element class \p FE this
* field is initialized to all zero, so that the variational
* formulation for an @e infinite element returns correct element
* matrices for a mesh using both finite and infinite elements.
*/
const std::vector<RealGradient>& get_dphase() const
{ return dphase; }
/**
* @returns the multiplicative weight at each quadrature point.
* This weight is used for certain infinite element weak
* formulations, so that @e weighted Sobolev spaces are
* used for the trial function space. This renders the
* variational form easily computable.
*
* In case of the general finite element class \p FE this
* field is initialized to all ones, so that the variational
* formulation for an @e infinite element returns correct element
* matrices for a mesh using both finite and infinite elements.
*/
const std::vector<Real>& get_Sobolev_weight() const
{ return weight; }
/**
* @returns the first global derivative of the multiplicative
* weight at each quadrature point. See \p get_Sobolev_weight()
* for details. In case of \p FE initialized to all zero.
*/
const std::vector<RealGradient>& get_Sobolev_dweight() const
{ return dweight; }
#endif
/**
* @returns the tangent vectors for face integration.
*/
const std::vector<std::vector<Point> >& get_tangents() const
{ return tangents; }
/**
* @returns the normal vectors for face integration.
*/
const std::vector<Point>& get_normals() const
{ return normals; }
/**
* @returns the curvatures for use in face integration.
*/
const std::vector<Real>& get_curvatures() const
{ return curvatures;}
/**
* Provides the class with the quadrature rule. Implement
* this in derived classes.
*/
virtual void attach_quadrature_rule (QBase* q) = 0;
/**
* @returns the total number of approximation shape functions
* for the current element. Useful during matrix assembly.
* Implement this in derived classes.
*/
virtual unsigned int n_shape_functions () const = 0;
/**
* @returns the total number of quadrature points. Useful
* during matrix assembly. Implement this in derived classes.
*/
virtual unsigned int n_quadrature_points () const = 0;
/**
* @returns the element type that the current shape functions
* have been calculated for. Useful in determining when shape
* functions must be recomputed.
*/
ElemType get_type() const { return elem_type; }
/**
* @returns the p refinement level that the current shape
* functions have been calculated for.
*/
unsigned int get_p_level() const { return _p_level; }
/**
* @returns the FE Type (approximation order and family) of the finite element.
*/
FEType get_fe_type() const { return fe_type; }
/**
* @returns the approximation order of the finite element.
*/
Order get_order() const { return static_cast<Order>(fe_type.order + _p_level); }
/**
* @returns the continuity level of the finite element.
*/
virtual FEContinuity get_continuity() const = 0;
/**
* @returns true if the finite element's higher order shape functions are
* hierarchic
*/
virtual bool is_hierarchic() const = 0;
/**
* @returns the finite element family of this element.
*/
FEFamily get_family() const { return fe_type.family; }
/**
* Prints the Jacobian times the weight for each quadrature point.
*/
void print_JxW(std::ostream& os) const;
/**
* Prints the value of each shape function at each quadrature point.
*/
void print_phi(std::ostream& os) const;
/**
* Prints the value of each shape function's derivative
* at each quadrature point.
*/
void print_dphi(std::ostream& os) const;
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
/**
* Prints the value of each shape function's second derivatives
* at each quadrature point.
*/
void print_d2phi(std::ostream& os) const;
#endif
/**
* Prints the spatial location of each quadrature point
* (on the physical element).
*/
void print_xyz(std::ostream& os) const;
/**
* Prints all the relevant information about the current element.
*/
void print_info(std::ostream& os) const;
/**
* Same as above, but allows you to print to a stream.
*/
friend std::ostream& operator << (std::ostream& os, const FEBase& fe);
protected:
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
/**
* Initialize the data fields for the base of an
* an infinite element. Implement this in the derived
* class \p FE<Dim,T>.
*/
virtual void init_base_shape_functions(const std::vector<Point>& qp,
const Elem* e) = 0;
#endif
/**
* Compute the jacobian and some other additional
* data fields. Takes the integration weights
* as input, along with a pointer to the element.
*/
virtual void compute_map(const std::vector<Real>& qw,
const Elem* e);
/**
* Compute the jacobian and some other additional
* data fields. Takes the integration weights
* as input, along with a pointer to the element.
* The element is assumed to have a constant Jacobian
*/
virtual void compute_affine_map(const std::vector<Real>& qw,
const Elem* e);
/**
* Compute the jacobian and some other additional
* data fields at the single point with index p.
*/
void compute_single_point_map(const std::vector<Real>& qw,
const Elem* e,
unsigned int p);
/**
* A utility function for use by compute_*_map
*/
void resize_map_vectors(unsigned int n_qp);
/**
* Same as compute_map, but for a side. Useful for boundary integration.
*/
void compute_face_map(const std::vector<Real>& qw,
const Elem* side);
/**
* Same as before, but for an edge. Useful for some projections.
*/
void compute_edge_map(const std::vector<Real>& qw,
const Elem* side);
/**
* After having updated the jacobian and the transformation
* from local to global coordinates in \p FEBase::compute_map(),
* the first derivatives of the shape functions are
* transformed to global coordinates, giving \p dphi,
* \p dphidx, \p dphidy, and \p dphidz. This method
* should rarely be re-defined in derived classes, but
* still should be usable for children. Therefore, keep
* it protected.
*/
virtual void compute_shape_functions(const Elem*);
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the x value of the pth entry of the dxzydxi_map.
*/
Real dxdxi_map(const unsigned int p) const { return dxyzdxi_map[p](0); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the y value of the pth entry of the dxzydxi_map.
*/
Real dydxi_map(const unsigned int p) const { return dxyzdxi_map[p](1); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the z value of the pth entry of the dxzydxi_map.
*/
Real dzdxi_map(const unsigned int p) const { return dxyzdxi_map[p](2); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the x value of the pth entry of the dxzydeta_map.
*/
Real dxdeta_map(const unsigned int p) const { return dxyzdeta_map[p](0); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the y value of the pth entry of the dxzydeta_map.
*/
Real dydeta_map(const unsigned int p) const { return dxyzdeta_map[p](1); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the z value of the pth entry of the dxzydeta_map.
*/
Real dzdeta_map(const unsigned int p) const { return dxyzdeta_map[p](2); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the x value of the pth entry of the dxzydzeta_map.
*/
Real dxdzeta_map(const unsigned int p) const { return dxyzdzeta_map[p](0); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the y value of the pth entry of the dxzydzeta_map.
*/
Real dydzeta_map(const unsigned int p) const { return dxyzdzeta_map[p](1); }
/**
* Used in \p FEBase::compute_map(), which should be
* be usable in derived classes, and therefore protected.
* Returns the z value of the pth entry of the dxzydzeta_map.
*/
Real dzdzeta_map(const unsigned int p) const { return dxyzdzeta_map[p](2); }
/**
* The dimensionality of the object
*/
const unsigned int dim;
/**
* The spatial locations of the quadrature points
*/
std::vector<Point> xyz;
/**
* Vector of parital derivatives:
* d(x)/d(xi), d(y)/d(xi), d(z)/d(xi)
*/
std::vector<RealGradient> dxyzdxi_map;
/**
* Vector of parital derivatives:
* d(x)/d(eta), d(y)/d(eta), d(z)/d(eta)
*/
std::vector<RealGradient> dxyzdeta_map;
/**
* Vector of parital derivatives:
* d(x)/d(zeta), d(y)/d(zeta), d(z)/d(zeta)
*/
std::vector<RealGradient> dxyzdzeta_map;
/**
* Vector of second partial derivatives in xi:
* d^2(x)/d(xi)^2, d^2(y)/d(xi)^2, d^2(z)/d(xi)^2
*/
std::vector<RealGradient> d2xyzdxi2_map;
/**
* Vector of mixed second partial derivatives in xi-eta:
* d^2(x)/d(xi)d(eta) d^2(y)/d(xi)d(eta) d^2(z)/d(xi)d(eta)
*/
std::vector<RealGradient> d2xyzdxideta_map;
/**
* Vector of second partial derivatives in eta:
* d^2(x)/d(eta)^2
*/
std::vector<RealGradient> d2xyzdeta2_map;
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
/**
* Vector of second partial derivatives in xi-zeta:
* d^2(x)/d(xi)d(zeta), d^2(y)/d(xi)d(zeta), d^2(z)/d(xi)d(zeta)
*/
std::vector<RealGradient> d2xyzdxidzeta_map;
/**
* Vector of mixed second partial derivatives in eta-zeta:
* d^2(x)/d(eta)d(zeta) d^2(y)/d(eta)d(zeta) d^2(z)/d(eta)d(zeta)
*/
std::vector<RealGradient> d2xyzdetadzeta_map;
/**
* Vector of second partial derivatives in zeta:
* d^2(x)/d(zeta)^2
*/
std::vector<RealGradient> d2xyzdzeta2_map;
#endif
/**
* Map for partial derivatives:
* d(xi)/d(x). Needed for the Jacobian.
*/
std::vector<Real> dxidx_map;
/**
* Map for partial derivatives:
* d(xi)/d(y). Needed for the Jacobian.
*/
std::vector<Real> dxidy_map;
/**
* Map for partial derivatives:
* d(xi)/d(z). Needed for the Jacobian.
*/
std::vector<Real> dxidz_map;
/**
* Map for partial derivatives:
* d(eta)/d(x). Needed for the Jacobian.
*/
std::vector<Real> detadx_map;
/**
* Map for partial derivatives:
* d(eta)/d(y). Needed for the Jacobian.
*/
std::vector<Real> detady_map;
/**
* Map for partial derivatives:
* d(eta)/d(z). Needed for the Jacobian.
*/
std::vector<Real> detadz_map;
/**
* Map for partial derivatives:
* d(zeta)/d(x). Needed for the Jacobian.
*/
std::vector<Real> dzetadx_map;
/**
* Map for partial derivatives:
* d(zeta)/d(y). Needed for the Jacobian.
*/
std::vector<Real> dzetady_map;
/**
* Map for partial derivatives:
* d(zeta)/d(z). Needed for the Jacobian.
*/
std::vector<Real> dzetadz_map;
/**
* Have calculations with this object already been started?
* Then all get_* functions should already have been called.
*/
mutable bool calculations_started;
/**
* Should we calculate shape functions?
*/
mutable bool calculate_phi;
/**
* Should we calculate shape function gradients?
*/
mutable bool calculate_dphi;
/**
* Should we calculate shape function hessians?
*/
mutable bool calculate_d2phi;
/**
* Shape function values.
*/
std::vector<std::vector<Real> > phi;
/**
* Shape function derivative values.
*/
std::vector<std::vector<RealGradient> > dphi;
/**
* Shape function derivatives in the xi direction.
*/
std::vector<std::vector<Real> > dphidxi;
/**
* Shape function derivatives in the eta direction.
*/
std::vector<std::vector<Real> > dphideta;
/**
* Shape function derivatives in the zeta direction.
*/
std::vector<std::vector<Real> > dphidzeta;
/**
* Shape function derivatives in the x direction.
*/
std::vector<std::vector<Real> > dphidx;
/**
* Shape function derivatives in the y direction.
*/
std::vector<std::vector<Real> > dphidy;
/**
* Shape function derivatives in the z direction.
*/
std::vector<std::vector<Real> > dphidz;
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
/**
* Shape function second derivative values.
*/
std::vector<std::vector<RealTensor> > d2phi;
/**
* Shape function second derivatives in the xi direction.
*/
std::vector<std::vector<Real> > d2phidxi2;
/**
* Shape function second derivatives in the xi-eta direction.
*/
std::vector<std::vector<Real> > d2phidxideta;
/**
* Shape function second derivatives in the xi-zeta direction.
*/
std::vector<std::vector<Real> > d2phidxidzeta;
/**
* Shape function second derivatives in the eta direction.
*/
std::vector<std::vector<Real> > d2phideta2;
/**
* Shape function second derivatives in the eta-zeta direction.
*/
std::vector<std::vector<Real> > d2phidetadzeta;
/**
* Shape function second derivatives in the zeta direction.
*/
std::vector<std::vector<Real> > d2phidzeta2;
/**
* Shape function second derivatives in the x direction.
*/
std::vector<std::vector<Real> > d2phidx2;
/**
* Shape function second derivatives in the x-y direction.
*/
std::vector<std::vector<Real> > d2phidxdy;
/**
* Shape function second derivatives in the x-z direction.
*/
std::vector<std::vector<Real> > d2phidxdz;
/**
* Shape function second derivatives in the y direction.
*/
std::vector<std::vector<Real> > d2phidy2;
/**
* Shape function second derivatives in the y-z direction.
*/
std::vector<std::vector<Real> > d2phidydz;
/**
* Shape function second derivatives in the z direction.
*/
std::vector<std::vector<Real> > d2phidz2;
#endif
/**
* Map for the shape function phi.
*/
std::vector<std::vector<Real> > phi_map;
/**
* Map for the derivative, d(phi)/d(xi).
*/
std::vector<std::vector<Real> > dphidxi_map;
/**
* Map for the derivative, d(phi)/d(eta).
*/
std::vector<std::vector<Real> > dphideta_map;
/**
* Map for the derivative, d(phi)/d(zeta).
*/
std::vector<std::vector<Real> > dphidzeta_map;
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
/**
* Map for the second derivative, d^2(phi)/d(xi)^2.
*/
std::vector<std::vector<Real> > d2phidxi2_map;
/**
* Map for the second derivative, d^2(phi)/d(xi)d(eta).
*/
std::vector<std::vector<Real> > d2phidxideta_map;
/**
* Map for the second derivative, d^2(phi)/d(xi)d(zeta).
*/
std::vector<std::vector<Real> > d2phidxidzeta_map;
/**
* Map for the second derivative, d^2(phi)/d(eta)^2.
*/
std::vector<std::vector<Real> > d2phideta2_map;
/**
* Map for the second derivative, d^2(phi)/d(eta)d(zeta).
*/
std::vector<std::vector<Real> > d2phidetadzeta_map;
/**
* Map for the second derivative, d^2(phi)/d(zeta)^2.
*/
std::vector<std::vector<Real> > d2phidzeta2_map;
#endif
/**
* Map for the side shape functions, psi.
*/
std::vector<std::vector<Real> > psi_map;
/**
* Map for the derivative of the side functions,
* d(psi)/d(xi).
*/
std::vector<std::vector<Real> > dpsidxi_map;
/**
* Map for the derivative of the side function,
* d(psi)/d(eta).
*/
std::vector<std::vector<Real> > dpsideta_map;
/**
* Map for the second derivatives (in xi) of the
* side shape functions. Useful for computing
* the curvature at the quadrature points.
*/
std::vector<std::vector<Real> > d2psidxi2_map;
/**
* Map for the second (cross) derivatives in xi, eta
* of the side shape functions. Useful for
* computing the curvature at the quadrature points.
*/
std::vector<std::vector<Real> > d2psidxideta_map;
/**
* Map for the second derivatives (in eta) of the
* side shape functions. Useful for computing the
* curvature at the quadrature points.
*/
std::vector<std::vector<Real> > d2psideta2_map;
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
//--------------------------------------------------------------
/* protected members for infinite elements, which are accessed
* from the outside through some inline functions
*/
/**
* Used for certain @e infinite element families:
* the first derivatives of the phase term in global coordinates,
* over @e all quadrature points.
*/
std::vector<RealGradient> dphase;
/**
* Used for certain @e infinite element families:
* the global derivative of the additional radial weight \f$ 1/{r^2} \f$,
* over @e all quadrature points.
*/
std::vector<RealGradient> dweight;
/**
* Used for certain @e infinite element families:
* the additional radial weight \f$ 1/{r^2} \f$ in local coordinates,
* over @e all quadrature points.
*/
std::vector<Real> weight;
#endif
/**
* Tangent vectors on boundary at quadrature points.
*/
std::vector<std::vector<Point> > tangents;
/**
* Normal vectors on boundary at quadrature points
*/
std::vector<Point> normals;
/**
* The mean curvature (= one half the sum of the principal
* curvatures) on the boundary at the quadrature points.
* The mean curvature is a scalar value.
*/
std::vector<Real> curvatures;
/**
* Jacobian*Weight values at quadrature points
*/
std::vector<Real> JxW;
/**
* The finite element type for this object. Note that this
* should be constant for the object.
*/
const FEType fe_type;
/**
* The element type the current data structures are
* set up for.
*/
ElemType elem_type;
/**
* The p refinement level the current data structures are
* set up for.
*/
unsigned int _p_level;
/**
* A pointer to the quadrature rule employed
*/
QBase* qrule;
/**
* A flag indicating if current data structures
* correspond to quadrature rule points
*/
bool shapes_on_quadrature;
private:
/**
* @returns \p true when the shape functions (for
* this \p FEFamily) depend on the particular
* element, and therefore needs to be re-initialized
* for each new element. \p false otherwise.
*/
virtual bool shapes_need_reinit() const = 0;
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
/**
* Make all \p InfFE<Dim,T_radial,T_map> classes friends
* so that they can safely used \p FE<Dim-1,T_base> through
* a \p FEBase* as base approximation.
*/
template <unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
friend class InfFE;
#endif
};
// ------------------------------------------------------------
// FEBase class inline members
inline
FEBase::FEBase(const unsigned int d,
const FEType& fet) :
dim(d),
xyz(),
dxyzdxi_map(),
dxyzdeta_map(),
dxyzdzeta_map(),
d2xyzdxi2_map(),
d2xyzdxideta_map(),
d2xyzdeta2_map(),
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
d2xyzdxidzeta_map(),
d2xyzdetadzeta_map(),
d2xyzdzeta2_map(),
#endif
dxidx_map(),
dxidy_map(),
dxidz_map(),
detadx_map(),
detady_map(),
detadz_map(),
dzetadx_map(),
dzetady_map(),
dzetadz_map(),
calculations_started(false),
calculate_phi(false),
calculate_dphi(false),
calculate_d2phi(false),
phi(),
dphi(),
dphidxi(),
dphideta(),
dphidzeta(),
dphidx(),
dphidy(),
dphidz(),
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
d2phi(),
d2phidxi2(),
d2phidxideta(),
d2phidxidzeta(),
d2phideta2(),
d2phidetadzeta(),
d2phidzeta2(),
d2phidx2(),
d2phidxdy(),
d2phidxdz(),
d2phidy2(),
d2phidydz(),
d2phidz2(),
#endif
phi_map(),
dphidxi_map(),
dphideta_map(),
dphidzeta_map(),
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
d2phidxi2_map(),
d2phidxideta_map(),
d2phidxidzeta_map(),
d2phideta2_map(),
d2phidetadzeta_map(),
d2phidzeta2_map(),
#endif
psi_map(),
dpsidxi_map(),
dpsideta_map(),
d2psidxi2_map(),
d2psidxideta_map(),
d2psideta2_map(),
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
dphase(),
dweight(),
weight(),
#endif
tangents(),
normals(),
curvatures(),
JxW(),
fe_type(fet),
elem_type(INVALID_ELEM),
_p_level(0),
qrule(NULL),
shapes_on_quadrature(false)
{
}
inline
FEBase::~FEBase()
{
}
} // namespace libMesh
#endif
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