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// $Id: fe_poly.h 20164 2009-11-25 05:22:16Z kanschat $
// Version: $Name$
//
// Copyright (C) 2004, 2005, 2006, 2007, 2009 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__fe_poly_h
#define __deal2__fe_poly_h
#include <fe/fe.h>
DEAL_II_NAMESPACE_OPEN
/*!@addtogroup febase */
/*@{*/
/**
* This class gives a unified framework for the implementation of
* FiniteElement classes based on a polynomial spaces like the
* TensorProductPolynomials or a PolynomialSpace classes.
*
* Every class conforming to the following interface can be used as
* template parameter POLY.
*
* @code
* static const unsigned int dimension;
*
* double compute_value (const unsigned int i,
* const Point<dim> &p) const;
*
* Tensor<1,dim> compute_grad (const unsigned int i,
* const Point<dim> &p) const;
*
* Tensor<2,dim> compute_grad_grad (const unsigned int i,
* const Point<dim> &p) const;
* @endcode
* Example classes are TensorProductPolynomials, PolynomialSpace or
* PolynomialsP.
*
* This class is not a fully implemented FiniteElement class. Instead
* there are several pure virtual functions declared in the
* FiniteElement and FiniteElement classes which cannot
* implemented by this class but are left for implementation in
* derived classes.
*
* Furthermore, this class assumes that shape functions of the
* FiniteElement under consideration do <em>not</em> depend on the
* actual shape of the cells in real space, i.e. update_once()
* includes <tt>update_values</tt>. For FiniteElements whose shape
* functions depend on the cells in real space, the update_once() and
* update_each() functions must be overloaded.
*
* @todo Since nearly all functions for spacedim != dim are
* specialized, this class needs cleaning up.
*
* @author Ralf Hartmann 2004, Guido Kanschat, 2009
**/
template <class POLY, int dim=POLY::dimension, int spacedim=dim>
class FE_Poly : public FiniteElement<dim,spacedim>
{
public:
/**
* Constructor.
*/
FE_Poly (const POLY& poly_space,
const FiniteElementData<dim> &fe_data,
const std::vector<bool> &restriction_is_additive_flags,
const std::vector<std::vector<bool> > &nonzero_components);
/**
* Return the polynomial degree
* of this finite element,
* i.e. the value passed to the
* constructor.
*/
unsigned int get_degree () const;
/**
* Return the value of the
* <tt>i</tt>th shape function at
* the point <tt>p</tt>. See the
* FiniteElement base class
* for more information about the
* semantics of this function.
*/
virtual double shape_value (const unsigned int i,
const Point<dim> &p) const;
/**
* Return the value of the
* <tt>component</tt>th vector
* component of the <tt>i</tt>th
* shape function at the point
* <tt>p</tt>. See the
* FiniteElement base class
* for more information about the
* semantics of this function.
*
* Since this element is scalar,
* the returned value is the same
* as if the function without the
* <tt>_component</tt> suffix
* were called, provided that the
* specified component is zero.
*/
virtual double shape_value_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Return the gradient of the
* <tt>i</tt>th shape function at
* the point <tt>p</tt>. See the
* FiniteElement base class
* for more information about the
* semantics of this function.
*/
virtual Tensor<1,dim> shape_grad (const unsigned int i,
const Point<dim> &p) const;
/**
* Return the gradient of the
* <tt>component</tt>th vector
* component of the <tt>i</tt>th
* shape function at the point
* <tt>p</tt>. See the
* FiniteElement base class
* for more information about the
* semantics of this function.
*
* Since this element is scalar,
* the returned value is the same
* as if the function without the
* <tt>_component</tt> suffix
* were called, provided that the
* specified component is zero.
*/
virtual Tensor<1,dim> shape_grad_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Return the tensor of second
* derivatives of the
* <tt>i</tt>th shape function at
* point <tt>p</tt> on the unit
* cell. See the
* FiniteElement base class
* for more information about the
* semantics of this function.
*/
virtual Tensor<2,dim> shape_grad_grad (const unsigned int i,
const Point<dim> &p) const;
/**
* Return the second derivative
* of the <tt>component</tt>th
* vector component of the
* <tt>i</tt>th shape function at
* the point <tt>p</tt>. See the
* FiniteElement base class
* for more information about the
* semantics of this function.
*
* Since this element is scalar,
* the returned value is the same
* as if the function without the
* <tt>_component</tt> suffix
* were called, provided that the
* specified component is zero.
*/
virtual Tensor<2,dim> shape_grad_grad_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Number of base elements in a
* mixed discretization. Since
* this is a scalar element,
* return one.
*/
virtual unsigned int n_base_elements () const;
/**
* Access to base element
* objects. Since this element is
* scalar,
* <tt>base_element(0)</tt> is
* <tt>this</tt>, and all other
* indices throw an error.
*/
virtual const FiniteElement<dim,spacedim> &
base_element (const unsigned int index) const;
/**
* Multiplicity of base element
* <tt>index</tt>. Since this is
* a scalar element,
* <tt>element_multiplicity(0)</tt>
* returns one, and all other
* indices will throw an error.
*/
virtual unsigned int element_multiplicity (const unsigned int index) const;
protected:
virtual
typename Mapping<dim,spacedim>::InternalDataBase *
get_data (const UpdateFlags,
const Mapping<dim,spacedim>& mapping,
const Quadrature<dim>& quadrature) const ;
virtual void
fill_fe_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Quadrature<dim> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim> &data,
CellSimilarity::Similarity &cell_similarity) const;
virtual void
fill_fe_face_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const Quadrature<dim-1> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim>& data) const ;
virtual void
fill_fe_subface_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int sub_no,
const Quadrature<dim-1> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim>& data) const ;
/**
* Determine the values that need
* to be computed on the unit
* cell to be able to compute all
* values required by
* <tt>flags</tt>.
*
* For the purpuse of this
* function, refer to the
* documentation in
* FiniteElement.
*
* This class assumes that shape
* functions of this
* FiniteElement do <em>not</em>
* depend on the actual shape of
* the cells in real
* space. Therefore, the effect
* in this element is as follows:
* if <tt>update_values</tt> is
* set in <tt>flags</tt>, copy it
* to the result. All other flags
* of the result are cleared,
* since everything else must be
* computed for each cell.
*/
virtual UpdateFlags update_once (const UpdateFlags flags) const;
/**
* Determine the values that need
* to be computed on every cell
* to be able to compute all
* values required by
* <tt>flags</tt>.
*
* For the purpuse of this
* function, refer to the
* documentation in
* FiniteElement.
*
* This class assumes that shape
* functions of this
* FiniteElement do <em>not</em>
* depend on the actual shape of
* the cells in real
* space.
*
* The effect in this element is
* as follows:
* <ul>
* <li> if
* <tt>update_gradients</tt> is
* set, the result will contain
* <tt>update_gradients</tt> and
* <tt>update_covariant_transformation</tt>.
* The latter is required to
* transform the gradient on the
* unit cell to the real
* cell. Remark, that the action
* required by
* <tt>update_covariant_transformation</tt>
* is actually performed by the
* Mapping object used in
* conjunction with this finite
* element. <li> if
* <tt>update_hessians</tt>
* is set, the result will
* contain
* <tt>update_hessians</tt>
* and
* <tt>update_covariant_transformation</tt>.
* The rationale is the same as
* above and no higher
* derivatives of the
* transformation are required,
* since we use difference
* quotients for the actual
* computation.
*
* </ul>
*/
virtual UpdateFlags update_each (const UpdateFlags flags) const;
/**
* Fields of cell-independent data.
*
* For information about the
* general purpose of this class,
* see the documentation of the
* base class.
*/
class InternalData : public FiniteElement<dim,spacedim>::InternalDataBase
{
public:
/**
* Array with shape function
* values in quadrature
* points. There is one
* row for each shape
* function, containing
* values for each quadrature
* point.
*
* In this array, we store
* the values of the shape
* function in the quadrature
* points on the unit
* cell. Since these values
* do not change under
* transformation to the real
* cell, we only need to copy
* them over when visiting a
* concrete cell.
*/
std::vector<std::vector<double> > shape_values;
/**
* Array with shape function
* gradients in quadrature
* points. There is one
* row for each shape
* function, containing
* values for each quadrature
* point.
*
* We store the gradients in
* the quadrature points on
* the unit cell. We then
* only have to apply the
* transformation (which is a
* matrix-vector
* multiplication) when
* visiting an actual cell.
*/
std::vector<std::vector<Tensor<1,dim> > > shape_gradients;
};
/**
* The polynomial space. Its type
* is given by the template
* parameter POLY.
*/
POLY poly_space;
};
/*@}*/
DEAL_II_NAMESPACE_CLOSE
#endif
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