/usr/include/deal.II/fe/fe_values.h is in libdeal.ii-dev 6.3.1-1.1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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4822 4823 | //---------------------------------------------------------------------------
// $Id: fe_values.h 21512 2010-07-17 03:24:43Z bangerth $
// Version: $Name: $
//
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 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_values_h
#define __deal2__fe_values_h
#include <base/config.h>
#include <base/exceptions.h>
#include <base/subscriptor.h>
#include <base/point.h>
#include <base/tensor.h>
#include <base/symmetric_tensor.h>
#include <base/vector_slice.h>
#include <base/quadrature.h>
#include <base/table.h>
#include <grid/tria.h>
#include <grid/tria_iterator.h>
#include <dofs/dof_handler.h>
#include <dofs/dof_accessor.h>
#include <hp/dof_handler.h>
#include <fe/fe.h>
#include <fe/fe_update_flags.h>
#include <fe/mapping.h>
#include <fe/mapping_q.h>
#include <multigrid/mg_dof_handler.h>
#include <multigrid/mg_dof_accessor.h>
#include <algorithm>
#include <memory>
// dummy include in order to have the
// definition of PetscScalar available
// without including other PETSc stuff
#ifdef DEAL_II_USE_PETSC
# include <petsc.h>
#endif
DEAL_II_NAMESPACE_OPEN
template <int dim> class Quadrature;
template <int dim, int spacedim=dim> class FEValuesBase;
template <typename Number> class Vector;
template <typename Number> class BlockVector;
namespace internal
{
/**
* A class whose specialization is
* used to define what type the
* curl of a vector valued function
* corresponds to.
*/
template <int dim>
struct CurlType;
/**
* A class whose specialization is
* used to define what type the
* curl of a vector valued function
* corresponds to.
*
* In 1d, the curl is a scalar.
*/
template <>
struct CurlType<1>{
typedef Tensor<1,1> type;
};
/**
* A class whose specialization is
* used to define what type the
* curl of a vector valued function
* corresponds to.
*
* In 2d, the curl is a scalar.
*/
template <>
struct CurlType<2>{
typedef Tensor<1,1> type;
};
/**
* A class whose specialization is
* used to define what type the
* curl of a vector valued function
* corresponds to.
*
* In 3d, the curl is a vector.
*/
template <>
struct CurlType<3>{
typedef Tensor<1,3> type;
};
}
/**
* A namespace in which we declare "extractors", i.e. classes that when used
* as subscripts in operator[] expressions on FEValues, FEFaceValues, and
* FESubfaceValues objects extract certain components of a vector-valued
* element. There are extractors for single scalar components,
* vector components consisting of <code>dim</code> elements,
* and second order symmetric tensors consisting
* of <code>(dim*dim + dim)/2</code> components
*
* See the description of the @ref vector_valued module for examples how to
* use the features of this namespace.
*
* @ingroup feaccess vector_valued
*/
namespace FEValuesExtractors
{
/**
* Extractor for a single scalar component
* of a vector-valued element. The concept
* of extractors is defined in the
* documentation of the namespace
* FEValuesExtractors and in the @ref
* vector_valued module.
*
* @ingroup feaccess vector_valued
*/
struct Scalar
{
/**
* The selected scalar component of the
* vector.
*/
unsigned int component;
/**
* Constructor. Take the selected
* vector component as argument.
*/
Scalar (const unsigned int component);
};
/**
* Extractor for a vector of
* <code>dim</code> components of a
* vector-valued element. The value of
* <code>dim</code> is defined by the
* FEValues object the extractor is applied
* to.
*
* The concept of
* extractors is defined in the
* documentation of the namespace
* FEValuesExtractors and in the @ref
* vector_valued module.
*
* @ingroup feaccess vector_valued
*/
struct Vector
{
/**
* The first component of the vector
* view.
*/
unsigned int first_vector_component;
/**
* Constructor. Take the first
* component of the selected vector
* inside the FEValues object as
* argument.
*/
Vector (const unsigned int first_vector_component);
};
/**
* Extractor for a symmetric tensor
* of a rank specified by the
* template argument. For a second
* order symmetric tensor, this
* represents a collection of
* <code>(dim*dim + dim)/2</code>
* components of a vector-valued
* element. The value of
* <code>dim</code> is defined by
* the FEValues object the
* extractor is applied to.
*
* The concept of
* extractors is defined in the
* documentation of the namespace
* FEValuesExtractors and in the @ref
* vector_valued module.
*
* @ingroup feaccess vector_valued
*
* @author Andrew McBride, 2009
*/
template <int rank>
struct SymmetricTensor
{
/**
* The first component of the tensor
* view.
*/
unsigned int first_tensor_component;
/**
* Constructor. Take the first
* component of the selected tensor
* inside the FEValues object as
* argument.
*/
SymmetricTensor (const unsigned int first_tensor_component);
};
}
/**
* A namespace for "views" on a FEValues, FEFaceValues, or FESubfaceValues
* object. A view represents only a certain part of the whole: whereas the
* FEValues object represents <i>all</i> values, gradients, or second
* derivatives of all components of a vector-valued element, views restrict
* the attention to only a single component or a subset of components.
*
* There are classes that present views for single scalar components,
* vector components consisting of <code>dim</code> elements, and
* symmetric second order tensor components
* consisting of <code>(dim*dim + dim)/2</code> elements
*
* See the description of the @ref vector_valued module for examples how to
* use the features of this namespace.
*
* @ingroup feaccess vector_valued
*/
namespace FEValuesViews
{
/**
* A class representing a view to a single
* scalar component of a possibly
* vector-valued finite element. Views are
* discussed in the @ref vector_valued module.
*
* @ingroup feaccess vector_valued
*/
template <int dim, int spacedim=dim>
class Scalar
{
public:
/**
* A typedef for the data type of
* values of the view this class
* represents. Since we deal with a
* single components, the value type is
* a scalar double.
*/
typedef double value_type;
/**
* A typedef for the type of gradients
* of the view this class
* represents. Here, for a scalar
* component of the finite element, the
* gradient is a
* <code>Tensor@<1,dim@></code>.
*/
typedef Tensor<1,spacedim> gradient_type;
/**
* A typedef for the type of second
* derivatives of the view this class
* represents. Here, for a scalar
* component of the finite element, the
* Hessian is a
* <code>Tensor@<2,dim@></code>.
*/
typedef Tensor<2,spacedim> hessian_type;
/**
* Default constructor. Creates an
* invalid object.
*/
Scalar ();
/**
* Constructor for an object that
* represents a single scalar component
* of a FEValuesBase object (or of one
* of the classes derived from
* FEValuesBase).
*/
Scalar (const FEValuesBase<dim,spacedim> &fe_values_base,
const unsigned int component);
/**
* Copy operator. This is not a
* lightweight object so we don't allow
* copying and generate an exception if
* this function is called.
*/
Scalar & operator= (const Scalar<dim,spacedim> &);
/**
* Return the value of the vector
* component selected by this view, for
* the shape function and quadrature
* point selected by the arguments.
*/
value_type
value (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the gradient (a tensor of
* rank 1) of the vector component
* selected by this view, for the shape
* function and quadrature point
* selected by the arguments.
*/
gradient_type
gradient (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the Hessian (the tensor of
* rank 2 of all second derivatives) of
* the vector component selected by
* this view, for the shape function
* and quadrature point selected by the
* arguments.
*/
hessian_type
hessian (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the values of the selected
* scalar component of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* This function is the equivalent of
* the
* FEValuesBase::get_function_values
* function but it only works on the
* selected scalar component.
*/
template <class InputVector>
void get_function_values (const InputVector& fe_function,
std::vector<value_type>& values) const;
/**
* Return the gradients of the selected
* scalar component of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* This function is the equivalent of
* the
* FEValuesBase::get_function_gradients
* function but it only works on the
* selected scalar component.
*/
template <class InputVector>
void get_function_gradients (const InputVector& fe_function,
std::vector<gradient_type>& gradients) const;
/**
* Return the Hessians of the selected
* scalar component of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* This function is the equivalent of
* the
* FEValuesBase::get_function_hessians
* function but it only works on the
* selected scalar component.
*/
template <class InputVector>
void get_function_hessians (const InputVector& fe_function,
std::vector<hessian_type>& hessians) const;
/**
* Return the Laplacians of the
* selected scalar component of
* the finite element function
* characterized by
* <tt>fe_function</tt> at the
* quadrature points of the
* cell, face or subface
* selected the last time the
* <tt>reinit</tt> function of
* the FEValues object was
* called, at the quadrature
* points. The Laplacians are
* the trace of the Hessians.
*
* This function is the
* equivalent of the
* FEValuesBase::get_function_laplacians
* function but it only works
* on the selected scalar
* component.
*/
template <class InputVector>
void get_function_laplacians (const InputVector& fe_function,
std::vector<value_type>& laplacians) const;
private:
/**
* A reference to the FEValuesBase object
* we operate on.
*/
const FEValuesBase<dim,spacedim> &fe_values;
/**
* The single scalar component this
* view represents of the FEValuesBase
* object.
*/
const unsigned int component;
/**
* A structure where for each shape
* function we pre-compute a bunch of
* data that will make later accesses
* much cheaper.
*/
struct ShapeFunctionData
{
/**
* For each shape function, store
* whether the selected vector
* component may be nonzero. For
* primitive shape functions we
* know for sure whether a certain
* scalar component of a given
* shape function is nonzero,
* whereas for non-primitive shape
* functions this may not be
* entirely clear (e.g. for RT
* elements it depends on the shape
* of a cell).
*/
bool is_nonzero_shape_function_component;
/**
* For each shape function, store
* the row index within the
* shape_values, shape_gradients,
* and shape_hessians tables (the
* column index is the quadrature
* point index). If the shape
* function is primitive, then we
* can get this information from
* the shape_function_to_row_table
* of the FEValues object;
* otherwise, we have to work a bit
* harder to compute this
* information.
*/
unsigned int row_index;
};
/**
* Store the data about shape
* functions.
*/
std::vector<ShapeFunctionData> shape_function_data;
};
/**
* A class representing a view to a set of
* <code>dim</code> components forming a
* vector part of a vector-valued finite
* element. Views are discussed in the
* @ref vector_valued module.
*
* @ingroup feaccess vector_valued
*/
template <int dim, int spacedim=dim>
class Vector
{
public:
/**
* A typedef for the data type of
* values of the view this class
* represents. Since we deal with a set
* of <code>dim</code> components, the
* value type is a Tensor<1,spacedim>.
*/
typedef Tensor<1,spacedim> value_type;
/**
* A typedef for the type of gradients
* of the view this class
* represents. Here, for a set of
* <code>dim</code> components of the
* finite element, the gradient is a
* <code>Tensor@<2,spacedim@></code>.
*/
typedef Tensor<2,spacedim> gradient_type;
/**
* A typedef for the type of
* symmetrized gradients of the view
* this class represents. Here, for a
* set of <code>dim</code> components
* of the finite element, the
* symmetrized gradient is a
* <code>SymmetricTensor@<2,spacedim@></code>.
*/
typedef dealii::SymmetricTensor<2,spacedim> symmetric_gradient_type;
/**
* A typedef for the type of the
* divergence of the view this class
* represents. Here, for a set of
* <code>dim</code> components of the
* finite element, the divergence of
* course is a scalar.
*/
typedef double divergence_type;
/**
* A typedef for the type of the
* curl of the view this class
* represents. Here, for a set of
* <code>spacedim=2</code> components
* of the finite element, the curl is
* a <code>Tensor@<1, 1@></code>. For
* <code>spacedim=3</code> it is a
* <code>Tensor@<1, dim@></code>.
*/
typedef typename internal::CurlType<spacedim>::type curl_type;
/**
* A typedef for the type of second
* derivatives of the view this class
* represents. Here, for a set of
* <code>dim</code> components of the
* finite element, the Hessian is a
* <code>Tensor@<3,dim@></code>.
*/
typedef Tensor<3,spacedim> hessian_type;
/**
* Default constructor. Creates an
* invalid object.
*/
Vector ();
/**
* Constructor for an object that
* represents dim components of a
* FEValuesBase object (or of one of
* the classes derived from
* FEValuesBase), representing a
* vector-valued variable.
*
* The second argument denotes the
* index of the first component of the
* selected vector.
*/
Vector (const FEValuesBase<dim,spacedim> &fe_values_base,
const unsigned int first_vector_component);
/**
* Copy operator. This is not a
* lightweight object so we don't allow
* copying and generate an exception if
* this function is called.
*/
Vector & operator= (const Vector<dim,spacedim> &);
/**
* Return the value of the vector
* components selected by this view,
* for the shape function and
* quadrature point selected by the
* arguments. Here, since the view
* represents a vector-valued part of
* the FEValues object with
* <code>dim</code> components, the
* return type is a tensor of rank 1
* with <code>dim</code> components.
*/
value_type
value (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the gradient (a tensor of
* rank 2) of the vector component
* selected by this view, for the shape
* function and quadrature point
* selected by the arguments.
*/
gradient_type
gradient (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the symmetric gradient (a
* symmetric tensor of rank 2) of the
* vector component selected by this
* view, for the shape function and
* quadrature point selected by the
* arguments.
*
* The symmetric gradient is defined as
* $\frac 12 [(\nabla \phi_i(x_q)) +
* (\nabla \phi_i(x_q))^T]$, where
* $\phi_i$ represents the
* <code>dim</code> components selected
* from the FEValuesBase object, and
* $x_q$ is the location of the $q$-th
* quadrature point.
*/
symmetric_gradient_type
symmetric_gradient (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the scalar divergence of
* the vector components selected by
* this view, for the shape function
* and quadrature point selected by the
* arguments.
*/
divergence_type
divergence (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the vector curl of
* the vector components selected by
* this view, for the shape function
* and quadrature point selected by the
* arguments. For 1d this function does
* not make any sense. Thus it is not
* implemented for <code>spacedim=1</code>.
* In 2d the curl is defined as
* @f{equation*}
* \operatorname{curl}(u):=\frac{du_2}{dx}
* -\frac{du_1}{dy},
* @f}
* whereas in 3d it is given by
* @f{equation*}
* \operatorname{curl}(u):=\left(
* \begin{array}{c}
* \frac{du_3}{dy}-\frac{du_2}{dz}\\
* \frac{du_1}{dz}-\frac{du_3}{dx}\\
* \frac{du_2}{dx}-\frac{du_1}{dy}
* \end{array}
* \right).
* @f}
*/
curl_type
curl (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the Hessian (the tensor of
* rank 2 of all second derivatives) of
* the vector components selected by
* this view, for the shape function
* and quadrature point selected by the
* arguments.
*/
hessian_type
hessian (const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the values of the selected
* vector components of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* This function is the equivalent of
* the
* FEValuesBase::get_function_values
* function but it only works on the
* selected vector components.
*/
template <class InputVector>
void get_function_values (const InputVector& fe_function,
std::vector<value_type>& values) const;
/**
* Return the gradients of the selected
* vector components of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* This function is the equivalent of
* the
* FEValuesBase::get_function_gradients
* function but it only works on the
* selected vector components.
*/
template <class InputVector>
void get_function_gradients (const InputVector& fe_function,
std::vector<gradient_type>& gradients) const;
/**
* Return the symmetrized gradients of
* the selected vector components of
* the finite element function
* characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* There is no equivalent function such
* as
* FEValuesBase::get_function_gradients
* in the FEValues classes but the
* information can be obtained from
* FEValuesBase::get_function_gradients,
* of course.
*/
template <class InputVector>
void get_function_symmetric_gradients (const InputVector& fe_function,
std::vector<symmetric_gradient_type>& symmetric_gradients) const;
/**
* Return the divergence of the selected
* vector components of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* There is no equivalent function such
* as
* FEValuesBase::get_function_gradients
* in the FEValues classes but the
* information can be obtained from
* FEValuesBase::get_function_gradients,
* of course.
*/
template <class InputVector>
void get_function_divergences (const InputVector& fe_function,
std::vector<divergence_type>& divergences) const;
/**
* Return the curl of the selected
* vector components of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* There is no equivalent function such
* as
* FEValuesBase::get_function_gradients
* in the FEValues classes but the
* information can be obtained from
* FEValuesBase::get_function_gradients,
* of course.
*/
template <class InputVector>
void get_function_curls (const InputVector& fe_function,
std::vector<curl_type>& curls) const;
/**
* Return the Hessians of the selected
* vector components of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* This function is the equivalent of
* the
* FEValuesBase::get_function_hessians
* function but it only works on the
* selected vector components.
*/
template <class InputVector>
void get_function_hessians (const InputVector& fe_function,
std::vector<hessian_type>& hessians) const;
/**
* Return the Laplacians of the
* selected vector components
* of the finite element
* function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the
* cell, face or subface
* selected the last time the
* <tt>reinit</tt> function of
* the FEValues object was
* called, at the quadrature
* points. The Laplacians are
* the trace of the Hessians.
*
* This function is the
* equivalent of the
* FEValuesBase::get_function_laplacians
* function but it only works
* on the selected vector
* components.
*/
template <class InputVector>
void get_function_laplacians (const InputVector& fe_function,
std::vector<value_type>& laplacians) const;
private:
/**
* A reference to the FEValuesBase object
* we operate on.
*/
const FEValuesBase<dim,spacedim> &fe_values;
/**
* The first component of the vector
* this view represents of the
* FEValuesBase object.
*/
const unsigned int first_vector_component;
/**
* A structure where for each shape
* function we pre-compute a bunch of
* data that will make later accesses
* much cheaper.
*/
struct ShapeFunctionData
{
/**
* For each pair (shape
* function,component within
* vector), store whether the
* selected vector component may be
* nonzero. For primitive shape
* functions we know for sure
* whether a certain scalar
* component of a given shape
* function is nonzero, whereas for
* non-primitive shape functions
* this may not be entirely clear
* (e.g. for RT elements it depends
* on the shape of a cell).
*/
bool is_nonzero_shape_function_component[dim];
/**
* For each pair (shape function,
* component within vector), store
* the row index within the
* shape_values, shape_gradients,
* and shape_hessians tables (the
* column index is the quadrature
* point index). If the shape
* function is primitive, then we
* can get this information from
* the shape_function_to_row_table
* of the FEValues object;
* otherwise, we have to work a bit
* harder to compute this
* information.
*/
unsigned int row_index[dim];
/**
* For each shape function say the
* following: if only a single
* entry in
* is_nonzero_shape_function_component
* for this shape function is
* nonzero, then store the
* corresponding value of row_index
* and
* single_nonzero_component_index
* represents the index between 0
* and dim for which it is
* attained. If multiple components
* are nonzero, then store -1. If
* no components are nonzero then
* store -2.
*/
int single_nonzero_component;
unsigned int single_nonzero_component_index;
};
/**
* Store the data about shape
* functions.
*/
std::vector<ShapeFunctionData> shape_function_data;
};
template <int rank, int dim, int spacedim = dim>
class SymmetricTensor;
/**
* A class representing a view to a set of
* <code>(dim*dim + dim)/2</code> components forming a
* symmetric second-order tensor from a
* vector-valued finite
* element. Views are discussed in the
* @ref vector_valued module.
*
* @ingroup feaccess vector_valued
*
* @author Andrew McBride, 2009
*/
template <int dim, int spacedim>
class SymmetricTensor<2,dim,spacedim>
{
public:
/**
* A typedef for the data type of
* values of the view this class
* represents. Since we deal with a set
* of <code>(dim*dim + dim)/2</code> components
* (i.e. the unique components of a symmetric second-order
* tensor), the value type is a SymmetricTensor<2,spacedim>.
*/
typedef dealii::SymmetricTensor<2, spacedim> value_type;
/**
* A typedef for the type of the
* divergence of the view this class
* represents. Here, for a set of
* of <code>(dim*dim + dim)/2</code> unique components
* of the finite element representing a symmetric second-order
* tensor, the divergence of
* course is a * <code>Tensor@<1,dim@></code>.
*/
typedef Tensor<1, spacedim> divergence_type;
/**
* Default constructor. Creates an
* invalid object.
*/
SymmetricTensor();
/**
* Constructor for an object that
* represents <code>(dim*dim + dim)/2</code>
* components of a
* FEValuesBase object (or of one of
* the classes derived from
* FEValuesBase), representing the unique
* components comprising a symmetric second-
* order tensor valued variable.
*
* The second argument denotes the
* index of the first component of the
* selected symmetric second order tensor.
*/
SymmetricTensor(const FEValuesBase<dim, spacedim> &fe_values_base,
const unsigned int first_tensor_component);
/**
* Copy operator. This is not a
* lightweight object so we don't allow
* copying and generate an exception if
* this function is called.
*/
SymmetricTensor & operator=(const SymmetricTensor<2, dim, spacedim> &);
/**
* Return the value of the vector
* components selected by this view,
* for the shape function and
* quadrature point selected by the
* arguments. Here, since the view
* represents a vector-valued part of
* the FEValues object with
* <code>(dim*dim + dim)/2</code> components
* (the unique components of a symmetric second-order tensor),
* the return type is a symmetric tensor of rank 2.
*/
value_type
value(const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the vector divergence of
* the vector components selected by
* this view, for the shape function
* and quadrature point selected by the
* arguments.
*/
divergence_type
divergence(const unsigned int shape_function,
const unsigned int q_point) const;
/**
* Return the values of the selected
* vector components of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* This function is the equivalent of
* the
* FEValuesBase::get_function_values
* function but it only works on the
* selected vector components.
*/
template <class InputVector>
void get_function_values(const InputVector& fe_function,
std::vector<value_type>& values) const;
/**
* Return the divergence of the selected
* vector components of the finite
* element function characterized by
* <tt>fe_function</tt> at the
* quadrature points of the cell, face
* or subface selected the last time
* the <tt>reinit</tt> function of the
* FEValues object was called, at the
* quadrature points.
*
* There is no equivalent function such
* as
* FEValuesBase::get_function_gradients
* in the FEValues classes but the
* information can be obtained from
* FEValuesBase::get_function_gradients,
* of course.
*/
template <class InputVector>
void get_function_divergences(const InputVector& fe_function,
std::vector<divergence_type>& divergences) const;
private:
/**
* A reference to the FEValuesBase object
* we operate on.
*/
const FEValuesBase<dim, spacedim> &fe_values;
/**
* The first component of the vector
* this view represents of the
* FEValuesBase object.
*/
const unsigned int first_tensor_component;
/**
* A structure where for each shape
* function we pre-compute a bunch of
* data that will make later accesses
* much cheaper.
*/
struct ShapeFunctionData
{
/**
* For each pair (shape
* function,component within
* vector), store whether the
* selected vector component may be
* nonzero. For primitive shape
* functions we know for sure
* whether a certain scalar
* component of a given shape
* function is nonzero, whereas for
* non-primitive shape functions
* this may not be entirely clear
* (e.g. for RT elements it depends
* on the shape of a cell).
*/
bool is_nonzero_shape_function_component[value_type::n_independent_components];
/**
* For each pair (shape function,
* component within vector), store
* the row index within the
* shape_values, shape_gradients,
* and shape_hessians tables (the
* column index is the quadrature
* point index). If the shape
* function is primitive, then we
* can get this information from
* the shape_function_to_row_table
* of the FEValues object;
* otherwise, we have to work a bit
* harder to compute this
* information.
*/
unsigned int row_index[value_type::n_independent_components];
/**
* For each shape function say the
* following: if only a single
* entry in
* is_nonzero_shape_function_component
* for this shape function is
* nonzero, then store the
* corresponding value of row_index
* and
* single_nonzero_component_index
* represents the index between 0
* and (dim^2 + dim)/2 for which it is
* attained. If multiple components
* are nonzero, then store -1. If
* no components are nonzero then
* store -2.
*/
int single_nonzero_component;
unsigned int single_nonzero_component_index;
};
/**
* Store the data about shape
* functions.
*/
std::vector<ShapeFunctionData> shape_function_data;
};
}
namespace internal
{
namespace FEValuesViews
{
/**
* A class objects of which store a
* collection of FEValuesViews::Scalar,
* FEValuesViews::Vector, etc object. The
* FEValuesBase class uses it to generate
* all possible Views classes upon
* construction time; we do this at
* construction time since the Views
* classes cache some information and are
* therefore relatively expensive to
* create.
*/
template <int dim, int spacedim>
struct Cache
{
/**
* Caches for scalar and
* vector, and symmetric second-order
* tensor valued views.
*/
std::vector<dealii::FEValuesViews::Scalar<dim,spacedim> > scalars;
std::vector<dealii::FEValuesViews::Vector<dim,spacedim> > vectors;
std::vector<dealii::FEValuesViews::SymmetricTensor<2,dim,spacedim> >
symmetric_second_order_tensors;
/**
* Constructor.
*/
Cache (const FEValuesBase<dim,spacedim> &fe_values);
};
}
}
/*!@addtogroup feaccess */
/*@{*/
//TODO: Add access to mapping values to FEValuesBase
//TODO: Several FEValuesBase of a system should share Mapping
/**
* Contains all data vectors for FEValues.
* This class has been extracted from FEValuesBase to be handed
* over to the fill functions of Mapping and
* FiniteElement.
*
* @note All data fields are public, but this is not
* critical, because access to this object is private in FEValues.
*
* The purpose of this class is discussed
* on the page on @ref UpdateFlagsEssay.
*
* @author Guido Kanschat, 2000
*/
template <int dim, int spacedim=dim>
class FEValuesData
{
public:
/**
* Initialize all vectors to
* correct size.
*/
void initialize (const unsigned int n_quadrature_points,
const FiniteElement<dim,spacedim> &fe,
const UpdateFlags flags);
/**
* Storage type for shape
* values. Each row in the matrix
* denotes the values of a single
* shape function at the
* different points, columns are
* for a single point with the
* different shape functions.
*
* If a shape function has more
* than one non-zero component
* (in deal.II diction: it is
* non-primitive), then we
* allocate one row per non-zero
* component, and shift
* subsequent rows backward.
* Lookup of the correct row for
* a shape function is thus
* simple in case the entire
* finite element is primitive
* (i.e. all shape functions are
* primitive), since then the
* shape function number equals
* the row number. Otherwise, use
* the
* #shape_function_to_row_table
* array to get at the first row
* that belongs to this
* particular shape function, and
* navigate among all the rows
* for this shape function using
* the
* FiniteElement::get_nonzero_components()
* function which tells us which
* components are non-zero and
* thus have a row in the array
* presently under discussion.
*/
typedef Table<2,double> ShapeVector;
/**
* Storage type for
* gradients. The layout of data
* is the same as for the
* #ShapeVector data type.
*/
typedef std::vector<std::vector<Tensor<1,spacedim> > > GradientVector;
/**
* Likewise for second order
* derivatives.
*/
typedef std::vector<std::vector<Tensor<2,spacedim> > > HessianVector;
/**
* Store the values of the shape
* functions at the quadrature
* points. See the description of
* the data type for the layout
* of the data in this field.
*/
ShapeVector shape_values;
/**
* Store the gradients of the
* shape functions at the
* quadrature points. See the
* description of the data type
* for the layout of the data in
* this field.
*/
GradientVector shape_gradients;
/**
* Store the 2nd derivatives of
* the shape functions at the
* quadrature points. See the
* description of the data type
* for the layout of the data in
* this field.
*/
HessianVector shape_hessians;
/**
* Store an array of weights
* times the Jacobi determinant
* at the quadrature points. This
* function is reset each time
* reinit() is called. The
* Jacobi determinant is actually
* the reciprocal value of the
* Jacobi matrices stored in this
* class, see the general
* documentation of this class
* for more information.
*
* However, if this object refers
* to an FEFaceValues or
* FESubfaceValues object, then
* the JxW_values correspond to
* the Jacobian of the
* transformation of the face,
* not the cell, i.e. the
* dimensionality is that of a
* surface measure, not of a
* volume measure. In this case,
* it is computed from the
* boundary forms, rather than
* the Jacobian matrix.
*/
std::vector<double> JxW_values;
/**
* Array of the Jacobian matrices at the
* quadrature points.
*/
std::vector<Tensor<2,spacedim> > jacobians;
/**
* Array of the derivatives of the Jacobian
* matrices at the quadrature points.
*/
std::vector<Tensor<3,spacedim> > jacobian_grads;
/**
* Array of the inverse Jacobian matrices
* at the quadrature points.
*/
std::vector<Tensor<2,spacedim> > inverse_jacobians;
/**
* Array of quadrature points. This array
* is set up upon calling reinit() and
* contains the quadrature points on the
* real element, rather than on the
* reference element.
*/
std::vector<Point<spacedim> > quadrature_points;
/**
* List of outward normal vectors at the
* quadrature points. This field is filled
* in by the finite element class.
*/
std::vector<Point<spacedim> > normal_vectors;
/**
* List of boundary forms at the
* quadrature points. This field is filled
* in by the finite element class.
*/
std::vector<Tensor<1,spacedim> > boundary_forms;
/**
* Indicate the first row which a
* given shape function occupies
* in the #shape_values,
* #shape_gradients and
* #shape_hessians
* arrays. If all shape functions
* are primitive, then this is
* the identity mapping. If, on
* the other hand some shape
* functions have more than one
* non-zero vector components,
* then they may occupy more than
* one row, and this array
* indicates which is the first
* one.
*
* The questions which particular
* vector component occupies
* which row for a given shape
* function is answered as
* follows: we allocate one row
* for each non-zero component as
* indicated by the
* FiniteElement::get_nonzero_components()
* function, and the rows are in
* ascending order exactly those
* non-zero components.
*/
std::vector<unsigned int> shape_function_to_row_table;
/**
* Original update flags handed
* to the constructor of
* FEValues.
*/
UpdateFlags update_flags;
};
/**
* FEValues, FEFaceValues and FESubfaceValues objects are interfaces to finite
* element and mapping classes on the one hand side, to cells and quadrature
* rules on the other side. They allow to evaluate values or derivatives of
* shape functions at the quadrature points of a quadrature formula when
* projected by a mapping from the unit cell onto a cell in real space. The
* reason for this abstraction is possible optimization: Depending on the type
* of finite element and mapping, some values can be computed once on the unit
* cell. Others must be computed on each cell, but maybe computation of
* several values at the same time offers ways for optimization. Since this
* interlay may be complex and depends on the actual finite element, it cannot
* be left to the applications programmer.
*
* FEValues, FEFaceValues and FESubfaceValues provide only data handling:
* computations are left to objects of type Mapping and FiniteElement. These
* provide functions <tt>get_*_data</tt> and <tt>fill_*_values</tt> which are
* called by the constructor and <tt>reinit</tt> functions of
* <tt>FEValues*</tt>, respectively.
*
* <h3>General usage</h3>
*
* Usually, an object of <tt>FEValues*</tt> is used in integration loops over
* all cells of a triangulation (or faces of cells). To take full advantage of
* the optimization features, it should be constructed before the loop so that
* information that does not depend on the location and shape of cells can be
* computed once and for all (this includes, for example, the values of shape
* functions at quadrature points for the most common elements: we can
* evaluate them on the unit cell and they will be the same when mapped to the
* real cell). Then, in the loop over all cells, it must be re-initialized for
* each grid cell to compute that part of the information that changes
* depending on the actual cell (for example, the gradient of shape functions
* equals the gradient on the unit cell -- which can be computed once and for
* all -- times the Jacobian matrix of the mapping between unit and real cell,
* which needs to be recomputed for each cell).
*
* A typical piece of code, adding up local contributions to the Laplace
* matrix looks like this:
*
* @code
* FEValues values (mapping, finite_element, quadrature, flags);
* for (cell = dof_handler.begin_active();
* cell != dof_handler.end();
* ++cell)
* {
* values.reinit(cell);
* for (unsigned int q=0; q<quadrature.size(); ++q)
* for (unsigned int i=0; i<finite_element.dofs_per_cell; ++i)
* for (unsigned int j=0; j<finite_element.dofs_per_cell; ++j)
* A(i,j) += fe_values.shape_value(i,q) *
* fe_values.shape_value(j,q) *
* fe_values.JxW(q);
* ...
* }
* @endcode
*
* The individual functions used here are described below. Note that by
* design, the order of quadrature points used inside the FEValues object is
* the same as defined by the quadrature formula passed to the constructor of
* the FEValues object above.
*
* <h3>Member functions</h3>
*
* The functions of this class fall into different cathegories:
* <ul>
* <li> shape_value(), shape_grad(), etc: return one of the values
* of this object at a time. These functions are inlined, so this
* is the suggested access to all finite element values. There
* should be no loss in performance with an optimizing compiler. If
* the finite element is vector valued, then these functions return
* the only non-zero component of the requested shape
* function. However, some finite elements have shape functions
* that have more than one non-zero component (we call them
* non-"primitive"), and in this case this set of functions will
* throw an exception since they cannot generate a useful
* result. Rather, use the next set of functions.
*
* <li> shape_value_component(), shape_grad_component(), etc:
* This is the same set of functions as above, except that for vector
* valued finite elements they return only one vector component. This
* is useful for elements of which shape functions have more than one
* non-zero component, since then the above functions cannot be used,
* and you have to walk over all (or only the non-zero) components of
* the shape function using this set of functions.
*
* <li> get_function_values(), get_function_gradients(), etc.: Compute a
* finite element function or its derivative in quadrature points.
*
* <li> reinit: initialize the FEValues object for a certain cell.
* This function is not in the present class but only in the derived
* classes and has a variable call syntax.
* See the docs for the derived classes for more information.
* </ul>
*
*
* <h3>UpdateFlags</h3>
*
* The UpdateFlags object handed to the constructor is used to
* determine, which of the data fields to compute. This way, it is
* possible to avoid expensive computations of useless derivatives.
* In the beginning, these flags are processed through the functions
* Mapping::update_once(), Mapping::update_each(),
* FiniteElement::update_once() FiniteElement::update_each(). All the
* results are bit-wise or'd and determine the fields actually
* computed. This enables Mapping and FiniteElement to schedule
* auxiliary data fields for updating. Still, it is recommended to
* give <b>all</b> needed update flags to FEValues.
*
* The mechanisms by which this class works is also discussed
* on the page on @ref UpdateFlagsEssay.
*
* @author Wolfgang Bangerth, 1998, 2003, Guido Kanschat, 2001
*/
template <int dim, int spacedim>
class FEValuesBase : protected FEValuesData<dim,spacedim>,
public Subscriptor
{
public:
/**
* Dimension in which this object
* operates.
*/
static const unsigned int dimension = dim;
/**
* Dimension of the space in
* which this object operates.
*/
static const unsigned int space_dimension = spacedim;
/**
* Number of quadrature points.
*/
const unsigned int n_quadrature_points;
/**
* Number of shape functions per
* cell. If we use this base
* class to evaluate a finite
* element on faces of cells,
* this is still the number of
* degrees of freedom per cell,
* not per face.
*/
const unsigned int dofs_per_cell;
/**
* Constructor. Set up the array
* sizes with <tt>n_q_points</tt>
* quadrature points, <tt>dofs_per_cell</tt>
* trial functions per cell and
* with the given pattern to
* update the fields when the
* <tt>reinit</tt> function of the
* derived classes is called. The
* fields themselves are not set
* up, this must happen in the
* constructor of the derived
* class.
*/
FEValuesBase (const unsigned int n_q_points,
const unsigned int dofs_per_cell,
const UpdateFlags update_flags,
const Mapping<dim,spacedim> &mapping,
const FiniteElement<dim,spacedim> &fe);
/**
* Destructor.
*/
~FEValuesBase ();
/// @name Extractors Methods to extract individual components
//@{
/**
* Create a view of the current FEValues
* object that represents a particular
* scalar component of the possibly
* vector-valued finite element. The
* concept of views is explained in the
* documentation of the namespace
* FEValuesViews and in particular
* in the @ref vector_valued module.
*/
const FEValuesViews::Scalar<dim,spacedim> &
operator[] (const FEValuesExtractors::Scalar &scalar) const;
/**
* Create a view of the current FEValues
* object that represents a set of
* <code>dim</code> scalar components
* (i.e. a vector) of the vector-valued
* finite element. The concept of views
* is explained in the documentation of
* the namespace FEValuesViews and in particular
* in the @ref vector_valued module.
*/
const FEValuesViews::Vector<dim,spacedim> &
operator[] (const FEValuesExtractors::Vector &vector) const;
/**
* Create a view of the current FEValues
* object that represents a set of
* <code>(dim*dim + dim)/2</code> scalar components
* (i.e. a symmetric 2nd order tensor)
* of the vector-valued
* finite element. The concept of views
* is explained in the documentation of
* the namespace FEValuesViews and in particular
* in the @ref vector_valued module.
*/
const FEValuesViews::SymmetricTensor<2,dim,spacedim> &
operator[] (const FEValuesExtractors::SymmetricTensor<2> &tensor) const;
//@}
/// @name ShapeAccess Access to shape function values
//@{
/**
* Value of a shape function at a
* quadrature point on the cell,
* face or subface selected the
* last time the <tt>reinit</tt>
* function of the derived class
* was called.
*
* If the shape function is
* vector-valued, then this
* returns the only non-zero
* component. If the shape
* function has more than one
* non-zero component (i.e. it is
* not primitive), then throw an
* exception of type
* ExcShapeFunctionNotPrimitive. In
* that case, use the
* shape_value_component()
* function.
*
* @arg function_no Number
* of the shape function to be
* computed
* @arg point_no Number of
* the quadrature point at which
* function is to be computed
*/
const double & shape_value (const unsigned int function_no,
const unsigned int point_no) const;
/**
* Compute one vector component of
* the value of a shape function
* at a quadrature point. If the
* finite element is scalar, then
* only component zero is allowed
* and the return value equals
* that of the shape_value()
* function. If the finite
* element is vector valued but
* all shape functions are
* primitive (i.e. they are
* non-zero in only one
* component), then the value
* returned by shape_value()
* equals that of this function
* for exactly one
* component. This function is
* therefore only of greater
* interest if the shape function
* is not primitive, but then it
* is necessary since the other
* function cannot be used.
*
* @arg function_no Number
* of the shape function to be
* computed
* @arg point_no Number of
* the quadrature point at which
* function is to be computed
* @arg component vector component to be computed
*/
double shape_value_component (const unsigned int function_no,
const unsigned int point_no,
const unsigned int component) const;
/**
* Compute the gradient of the
* <tt>i</tt>th shape function at the
* <tt>j</tt>th quadrature point with
* respect to real cell
* coordinates. If you want to
* get the derivative in one of
* the coordinate directions, use
* the appropriate function of
* the Tensor class to
* extract one component. Since
* only a reference to the
* gradient's value is returned,
* there should be no major
* performance drawback.
*
* If the shape function is
* vector-valued, then this
* returns the only non-zero
* component. If the shape
* function has more than one
* non-zero component (i.e. it is
* not primitive), then throw an
* exception of type
* ExcShapeFunctionNotPrimitive. In
* that case, use the
* shape_grad_component()
* function.
*/
const Tensor<1,spacedim> &
shape_grad (const unsigned int function,
const unsigned int quadrature_point) const;
/**
* Return one vector component of
* the gradient of a shape function
* at a quadrature point. If the
* finite element is scalar, then
* only component zero is allowed
* and the return value equals
* that of the shape_grad()
* function. If the finite
* element is vector valued but
* all shape functions are
* primitive (i.e. they are
* non-zero in only one
* component), then the value
* returned by shape_grad()
* equals that of this function
* for exactly one
* component. This function is
* therefore only of greater
* interest if the shape function
* is not primitive, but then it
* is necessary since the other
* function cannot be used.
*/
Tensor<1,spacedim>
shape_grad_component (const unsigned int function_no,
const unsigned int point_no,
const unsigned int component) const;
/**
* Second derivatives of
* the <tt>function_no</tt>th shape function at
* the <tt>point_no</tt>th quadrature point
* with respect to real cell
* coordinates. If you want to
* get the derivatives in one of
* the coordinate directions, use
* the appropriate function of
* the Tensor class to
* extract one component. Since
* only a reference to the
* derivative values is returned,
* there should be no major
* performance drawback.
*
* If the shape function is
* vector-valued, then this
* returns the only non-zero
* component. If the shape
* function has more than one
* non-zero component (i.e. it is
* not primitive), then throw an
* exception of type
* ExcShapeFunctionNotPrimitive. In
* that case, use the
* shape_grad_grad_component()
* function.
*/
const Tensor<2,spacedim> &
shape_hessian (const unsigned int function_no,
const unsigned int point_no) const;
/**
* @deprecated Wrapper for shape_hessian()
*/
const Tensor<2,spacedim> &
shape_2nd_derivative (const unsigned int function_no,
const unsigned int point_no) const;
/**
* Return one vector component of
* the gradient of a shape
* function at a quadrature
* point. If the finite element
* is scalar, then only component
* zero is allowed and the return
* value equals that of the
* shape_hessian()
* function. If the finite
* element is vector valued but
* all shape functions are
* primitive (i.e. they are
* non-zero in only one
* component), then the value
* returned by
* shape_hessian()
* equals that of this function
* for exactly one
* component. This function is
* therefore only of greater
* interest if the shape function
* is not primitive, but then it
* is necessary since the other
* function cannot be used.
*/
Tensor<2,spacedim>
shape_hessian_component (const unsigned int function_no,
const unsigned int point_no,
const unsigned int component) const;
/**
* @deprecated Wrapper for shape_hessian_component()
*/
Tensor<2,spacedim>
shape_2nd_derivative_component (const unsigned int function_no,
const unsigned int point_no,
const unsigned int component) const;
//@}
/// @name FunctionAccess Access to values of global finite element functions
//@{
/**
* Returns the values of the
* finite element function
* characterized by
* <tt>fe_function</tt> restricted to
* the cell, face or subface
* selected the last time the
* <tt>reinit</tt> function of the
* derived class was called, at
* the quadrature points.
*
* If the present cell is not an
* active one the interpolated
* function values are returned.
*
* To get values of
* multi-component elements,
* there is another
* get_function_values() below,
* returning a vector of vectors
* of results.
*
* This function may only be used if the
* finite element in use is a scalar one,
* i.e. has only one vector component. If
* it is a vector-valued one, then use
* the other get_function_values()
* function.
*
* The function assumes that the
* <tt>values</tt> object already has the
* correct size.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*/
template <class InputVector, typename number>
void get_function_values (const InputVector& fe_function,
std::vector<number>& values) const;
/**
* Access to vector valued finite
* element functions.
*
* This function does the same as
* the other
* get_function_values(), but
* applied to multi-component
* elements.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*/
template <class InputVector, typename number>
void get_function_values (const InputVector &fe_function,
std::vector<Vector<number> > &values) const;
/**
* Generate function values from
* an arbitrary vector.
*
* This function offers the
* possibility to extract
* function values in quadrature
* points from vectors not
* corresponding to a whole
* discretization.
*
* The vector <tt>indices</tt>
* corresponds to the degrees of
* freedom on a single cell. Its
* length may even be a multiple
* of the number of dofs per
* cell. Then, the vectors in
* <tt>value</tt> should allow
* for the same multiple of the
* components of the finite
* element.
*
* You may want to use this
* function, if you want to
* access just a single block
* from a BlockVector, if you
* have a multi-level vector or
* if you already have a local
* representation of your finite
* element data.
*/
template <class InputVector, typename number>
void get_function_values (const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<number>& values) const;
/**
* Generate vector function
* values from an arbitrary
* vector.
*
* This function offers the
* possibility to extract
* function values in quadrature
* points from vectors not
* corresponding to a whole
* discretization.
*
* The vector <tt>indices</tt>
* corresponds to the degrees of
* freedom on a single cell. Its
* length may even be a multiple
* of the number of dofs per
* cell. Then, the vectors in
* <tt>value</tt> should allow
* for the same multiple of the
* components of the finite
* element.
*
* You may want to use this
* function, if you want to
* access just a single block
* from a BlockVector, if you
* have a multi-level vector or
* if you already have a local
* representation of your finite
* element data.
*
* Since this function allows for
* fairly general combinations of
* argument sizes, be aware that
* the checks on the arguments
* may not detect errors.
*/
template <class InputVector, typename number>
void get_function_values (const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<Vector<number> >& values) const;
/**
* Generate vector function
* values from an arbitrary
* vector.
*
* This function offers the
* possibility to extract
* function values in quadrature
* points from vectors not
* corresponding to a whole
* discretization.
*
* The vector <tt>indices</tt>
* corresponds to the degrees of
* freedom on a single cell. Its
* length may even be a multiple
* of the number of dofs per
* cell. Then, the vectors in
* <tt>value</tt> should allow
* for the same multiple of the
* components of the finite
* element.
*
* Depending on the value of the last
* argument, the outer vector of
* <tt>values</tt> has either the
* length of the quadrature rule
* (<tt>quadrature_points_fastest
* == false</tt>) or the length
* of components to be filled
* <tt>quadrature_points_fastest
* == true</tt>. If <tt>p</tt> is
* the current quadrature point
* number and <tt>i</tt> is the
* vector component of the
* solution desired, the access
* to <tt>values</tt> is
* <tt>values[p][i]</tt> if
* <tt>quadrature_points_fastest
* == false</tt>, and
* <tt>values[i][p]</tt>
* otherwise.
*
* You may want to use this
* function, if you want to
* access just a single block
* from a BlockVector, if you
* have a multi-level vector or
* if you already have a local
* representation of your finite
* element data.
*
* Since this function allows for
* fairly general combinations of
* argument sizes, be aware that
* the checks on the arguments
* may not detect errors.
*/
template <class InputVector>
void get_function_values (const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
VectorSlice<std::vector<std::vector<double> > > values,
const bool quadrature_points_fastest) const;
/**
* Compute the gradients of the finite
* element function characterized
* by @p fe_function restricted to
* @p cell at the quadrature points.
*
* If the present cell is not an active
* one the interpolated function values
* are returned.
*
* This function may only be used if the
* finite element in use is a scalar one,
* i.e. has only one vector component. If
* it is a vector-valued one, then use
* the other get_function_gradients()
* function.
*
* The function assumes that the
* @p gradients object already has the
* right size.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*
* The output are the gradients
* of the function represented by
* these DoF values, as computed
* in real space (as opposed to
* on the unit cell).
*/
template <class InputVector>
void get_function_gradients (const InputVector &fe_function,
std::vector<Tensor<1,spacedim> > &gradients) const;
/**
* @deprecated Use
* get_function_gradients() instead.
*/
template <class InputVector>
void get_function_grads (const InputVector &fe_function,
std::vector<Tensor<1,spacedim> > &gradients) const;
/**
* Compute the gradients of the finite
* element function characterized
* by @p fe_function restricted to
* @p cell at the quadrature points.
*
* If the present cell is not an active
* one the interpolated function values
* are returned.
*
* The function assumes that the
* @p gradients object already has the
* right size.
*
* This function does the same as
* the other get_function_values(),
* but applied to multi-component
* elements.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*
* The output are the gradients
* of the function represented by
* these DoF values, as computed
* in real space (as opposed to
* on the unit cell).
*/
template <class InputVector>
void get_function_gradients (const InputVector &fe_function,
std::vector<std::vector<Tensor<1,spacedim> > > &gradients) const;
/**
* @deprecated Use
* get_function_gradients() instead.
*/
template <class InputVector>
void get_function_grads (const InputVector &fe_function,
std::vector<std::vector<Tensor<1,spacedim> > > &gradients) const;
/**
* Function gradient access with
* more flexibility. see
* get_function_values() with
* corresponding arguments.
*/
template <class InputVector>
void get_function_gradients (const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<Tensor<1,spacedim> >& gradients) const;
/**
* @deprecated Use
* get_function_gradients() instead.
*/
template <class InputVector>
void get_function_grads (const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<Tensor<1,spacedim> >& gradients) const;
/**
* Function gradient access with
* more flexibility. see
* get_function_values() with
* corresponding arguments.
*/
template <class InputVector>
void get_function_gradients (const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
VectorSlice<std::vector<std::vector<Tensor<1,spacedim> > > > gradients,
bool quadrature_points_fastest = false) const;
/**
* @deprecated Use
* get_function_gradients() instead.
*/
template <class InputVector>
void get_function_grads (const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<std::vector<Tensor<1,spacedim> > >& gradients,
bool quadrature_points_fastest = false) const;
/**
* Compute the tensor of second
* derivatives of the finite
* element function characterized
* by @p fe_function restricted
* to @p cell at the quadrature
* points.
*
* The function assumes that the
* @p hessians object
* already has the correct size.
*
* This function may only be used if the
* finite element in use is a scalar one,
* i.e. has only one vector component. If
* it is a vector-valued one, then use
* the other
* get_function_hessians()
* function.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*
* The output are the second
* derivatives of the function
* represented by these DoF
* values, as computed in real
* space (as opposed to on the
* unit cell).
*/
template <class InputVector>
void
get_function_hessians (const InputVector& fe_function,
std::vector<Tensor<2,spacedim> >& hessians) const;
/**
* Compute the tensor of second
* derivatives of the finite
* element function characterized
* by @p fe_function restricted to
* @p cell at the quadrature points.
*
* The function assumes that the
* @p hessians object already has
* the right size.
*
* This function does the same as
* the other one with the same
* name, but applies to
* vector-valued finite elements.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*
* The output are the second derivatives
* of the function represented by
* these DoF values, as computed
* in real space (as opposed to
* on the unit cell).
*/
template <class InputVector>
void
get_function_hessians (const InputVector &fe_function,
std::vector<std::vector<Tensor<2,spacedim> > > &hessians,
bool quadrature_points_fastest = false) const;
/**
* Access to the second
* derivatives of a function with
* more flexibility. see
* get_function_values() with
* corresponding arguments.
*/
template <class InputVector>
void get_function_hessians (
const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<Tensor<2,spacedim> >& hessians) const;
/**
* Access to the second
* derivatives of a function with
* more flexibility. see
* get_function_values() with
* corresponding arguments.
*/
template <class InputVector>
void get_function_hessians (
const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
VectorSlice<std::vector<std::vector<Tensor<2,spacedim> > > > hessians,
bool quadrature_points_fastest = false) const;
/**
* @deprecated Wrapper for get_function_hessians()
*/
template <class InputVector>
void
get_function_2nd_derivatives (const InputVector&,
std::vector<Tensor<2,spacedim> >&) const;
/**
* @deprecated Wrapper for get_function_hessians()
*/
template <class InputVector>
void
get_function_2nd_derivatives (const InputVector&,
std::vector<std::vector<Tensor<2,spacedim> > >&,
bool = false) const;
/**
* Compute the (scalar) Laplacian
* of the finite element function
* characterized by @p
* fe_function restricted to @p
* cell at the quadrature
* points. The Laplacian output
* vector is equivalent to
* getting
* <tt>trace(hessians)</tt>,
* where <tt>hessian</tt> would
* be the output of the
* get_function_hessians()
* function.
*
* The function assumes that the
* @p laplacians object
* already has the correct size.
*
* This function may only be used if the
* finite element in use is a scalar one,
* i.e. has only one vector component. If
* it is a vector-valued one, then use
* the other
* get_function_laplacians()
* function.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*
* The output are the traces of
* the second derivatives
* (i.e. Laplacians) of the
* function represented by these
* DoF values, as computed in
* real space (as opposed to on
* the unit cell).
*/
template <class InputVector, typename number>
void
get_function_laplacians (const InputVector& fe_function,
std::vector<number>& laplacians) const;
/**
* Compute the (scalar) Laplacian
* of the finite element function
* characterized by @p
* fe_function restricted to @p
* cell at the quadrature
* points. The Laplacian output
* vector is equivalent to
* getting
* <tt>trace(hessians)</tt>, with
* <tt>hessian</tt> corresponding
* to the output of the
* get_function_hessians()
* function.
*
* The function assumes that the
* @p laplacians object
* already has the correct size.
*
* This function does the same as
* the other one with the same
* name, but applies to
* vector-valued finite elements.
*
* The actual data type of the
* input vector may be either a
* Vector<T>,
* BlockVector<T>, or one
* of the sequential PETSc or
* Trilinos vector wrapper
* classes. It represents a
* global vector of DoF values
* associated with the DofHandler
* object with which this
* FEValues object was last
* initialized.
*
* The output are the traces of
* the second derivatives (i.e.
* Laplacians) of the function
* represented by these DoF
* values, as computed in real
* space (as opposed to on the
* unit cell).
*/
template <class InputVector, typename number>
void
get_function_laplacians (const InputVector &fe_function,
std::vector<Vector<number> > &laplacians) const;
/**
* Access to the second
* derivatives of a function with
* more flexibility. see
* get_function_values() with
* corresponding arguments.
*/
template <class InputVector, typename number>
void get_function_laplacians (
const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<number>& laplacians) const;
/**
* Access to the second
* derivatives of a function with
* more flexibility. see
* get_function_values() with
* corresponding arguments.
*/
template <class InputVector, typename number>
void get_function_laplacians (
const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<Vector<number> >& laplacians) const;
/**
* Access to the second
* derivatives of a function with
* more flexibility. see
* get_function_values() with
* corresponding arguments.
*/
template <class InputVector, typename number>
void get_function_laplacians (
const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<std::vector<number> >& laplacians,
bool quadrature_points_fastest = false) const;
//@}
/**
* Position of the <tt>i</tt>th
* quadrature point in real space.
*/
const Point<spacedim> & quadrature_point (const unsigned int i) const;
/**
* Return a pointer to the vector of
* quadrature points.
*/
const std::vector<Point<spacedim> > & get_quadrature_points () const;
/**
* Mapped quadrature weight. If
* this object refers to a volume
* evaluation (i.e. the derived
* class is of type FEValues),
* then this is the Jacobi
* determinant times the weight
* of the *<tt>i</tt>th unit
* quadrature point.
*
* For surface evaluations
* (i.e. classes FEFaceValues or
* FESubfaceValues), it is the
* mapped surface element times
* the weight of the quadrature
* point.
*
* You can think of the quantity returned
* by this function as the volume or
* surface element $dx, ds$ in the
* integral that we implement here by
* quadrature.
*/
double JxW (const unsigned int quadrature_point) const;
/**
* Pointer to the array holding
* the values returned by JxW().
*/
const std::vector<double> & get_JxW_values () const;
/**
* Return the Jacobian of the
* transformation at the specified
* quadrature point, i.e.
* $J_{ij}=dx_i/d\hat x_j$
*/
const Tensor<2,spacedim> & jacobian (const unsigned int quadrature_point) const;
/**
* Pointer to the array holding
* the values returned by jacobian().
*/
const std::vector<Tensor<2,spacedim> > & get_jacobians () const;
/**
* Return the second derivative of the
* transformation from unit to real cell,
* i.e. the first derivative of the
* Jacobian, at the specified quadrature
* point, i.e. $G_{ijk}=dJ_{jk}/d\hat x_i$.
*/
const Tensor<3,spacedim> & jacobian_grad (const unsigned int quadrature_point) const;
/**
* Pointer to the array holding
* the values returned by
* jacobian_grads().
*/
const std::vector<Tensor<3,spacedim> > & get_jacobian_grads () const;
/**
* Return the inverse Jacobian of the
* transformation at the specified
* quadrature point, i.e.
* $J_{ij}=d\hat x_i/dx_j$
*/
const Tensor<2,spacedim> & inverse_jacobian (const unsigned int quadrature_point) const;
/**
* Pointer to the array holding
* the values returned by
* inverse_jacobian().
*/
const std::vector<Tensor<2,spacedim> > & get_inverse_jacobians () const;
/**
* Constant reference to the
* selected mapping object.
*/
const Mapping<dim,spacedim> & get_mapping () const;
/**
* Constant reference to the
* selected finite element
* object.
*/
const FiniteElement<dim,spacedim> & get_fe () const;
/**
* Return the update flags set
* for this object.
*/
UpdateFlags get_update_flags () const;
/**
* Return a triangulation
* iterator to the current cell.
*/
const typename Triangulation<dim,spacedim>::cell_iterator get_cell () const;
/**
* For a face, return the outward
* normal vector to the cell at
* the <tt>i</tt>th quadrature
* point.
*
* For a cell of codimension one,
* return the normal vector, as
* it is specified by the
* numbering of the vertices.
*
* The length of the vector
* is normalized to one.
*/
const Point<spacedim> & normal_vector (const unsigned int i) const;
/**
* Return the normal vectors at
* the quadrature points. For a
* face, these are the outward
* normal vectors to the
* cell. For a cell of
* codimension one, the
* orientation is given by the
* numbering of vertices.
*/
const std::vector<Point<spacedim> > & get_normal_vectors () const;
/**
* @deprecated Use
* normal_vector() instead.
*
* Return the outward normal vector to
* the cell at the <tt>i</tt>th quadrature
* point. The length of the vector
* is normalized to one.
*/
const Point<spacedim> & cell_normal_vector (const unsigned int i) const;
/**
* @deprecated Use
* get_normal_vectors() instead.
*
* Returns the vectors normal to
* the cell in each of the
* quadrature points.
*/
const std::vector<Point<spacedim> > & get_cell_normal_vectors () const;
/**
* Return the relation of the current
* cell to the previous cell. This
* allows re-use of some cell data
* (like local matrices for equations
* with constant coefficients) if the
* result is
* <tt>CellSimilarity::translation</tt>.
*/
CellSimilarity::Similarity get_cell_similarity () const;
/**
* Determine an estimate for the
* memory consumption (in bytes)
* of this object.
*/
unsigned int memory_consumption () const;
/**
* This exception is thrown if
* FEValuesBase is asked to
* return the value of a field
* which was not required by the
* UpdateFlags for this
* FEValuesBase.
*
* @ingroup Exceptions
*/
DeclException0 (ExcAccessToUninitializedField);
/**
* @todo Document this
*
* @ingroup Exceptions
*/
DeclException0 (ExcCannotInitializeField);
/**
* @todo Document this
*
* @ingroup Exceptions
*/
DeclException0 (ExcInvalidUpdateFlag);
/**
* @todo Document this
*
* @ingroup Exceptions
*/
DeclException0 (ExcFEDontMatch);
/**
* @todo Document this
*
* @ingroup Exceptions
*/
DeclException1 (ExcShapeFunctionNotPrimitive,
int,
<< "The shape function with index " << arg1
<< " is not primitive, i.e. it is vector-valued and "
<< "has more than one non-zero vector component. This "
<< "function cannot be called for these shape functions. "
<< "Maybe you want to use the same function with the "
<< "_component suffix?");
/**
* @todo Document this
*
* @ingroup Exceptions
*/
DeclException0 (ExcFENotPrimitive);
protected:
/**
* Objects of the FEValues
* class need to store a pointer
* (i.e. an iterator) to the
* present cell in order to be
* able to extract the values of
* the degrees of freedom on this
* cell in the
* get_function_values() and
* assorted functions. On the
* other hand, this class should
* also work for different
* iterators, as long as they
* have the same interface to
* extract the DoF values (i.e.,
* for example, they need to have
* a @p get_interpolated_dof_values
* function).
*
* This calls for a common base
* class of iterator classes, and
* making the functions we need
* here @p virtual. On the other
* hand, this is the only place
* in the library where we need
* this, and introducing a base
* class of iterators and making
* a function virtual penalizes
* <em>all</em> users of the
* iterators, which are basically
* intended as very fast accessor
* functions. So we do not want
* to do this. Rather, what we do
* here is making the functions
* we need virtual only for use
* with <em>this class</em>. The idea
* is the following: have a
* common base class which
* declares some pure virtual
* functions, and for each
* possible iterator type, we
* have a derived class which
* stores the iterator to the
* cell and implements these
* functions. Since the iterator
* classes have the same
* interface, we can make the
* derived classes a template,
* templatized on the iterator
* type.
*
* This way, the use of virtual
* functions is restricted to
* only this class, and other
* users of iterators do not have
* to bear the negative effects.
*
* @author Wolfgang Bangerth, 2003
*/
class CellIteratorBase;
/**
* Forward declaration of classes derived
* from CellIteratorBase. Their
* definition and implementation is given
* in the .cc file.
*/
template <typename CI> class CellIterator;
class TriaCellIterator;
/**
* Store the cell selected last time the
* reinit() function was called. This is
* necessary for the
* <tt>get_function_*</tt> functions as
* well as the functions of same name in
* the extractor classes.
*/
std::auto_ptr<const CellIteratorBase> present_cell;
/**
* Storage for the mapping object.
*/
const SmartPointer<const Mapping<dim,spacedim>,FEValuesBase<dim,spacedim> > mapping;
/**
* Store the finite element for later use.
*/
const SmartPointer<const FiniteElement<dim,spacedim>,FEValuesBase<dim,spacedim> > fe;
/**
* Internal data of mapping.
*/
SmartPointer<typename Mapping<dim,spacedim>::InternalDataBase,FEValuesBase<dim,spacedim> > mapping_data;
/**
* Internal data of finite element.
*/
SmartPointer<typename Mapping<dim,spacedim>::InternalDataBase,FEValuesBase<dim,spacedim> > fe_data;
/**
* Initialize some update
* flags. Called from the
* @p initialize functions of
* derived classes, which are in
* turn called from their
* constructors.
*
* Basically, this function finds
* out using the finite element
* and mapping object already
* stored which flags need to be
* set to compute everything the
* user wants, as expressed
* through the flags passed as
* argument.
*/
UpdateFlags compute_update_flags (const UpdateFlags update_flags) const;
/**
* An enum variable that can store
* different states of the current cell
* in comparison to the previously
* visited cell. If wanted, additional
* states can be checked here and used
* in one of the methods used during
* reinit.
*/
CellSimilarity::Similarity cell_similarity;
/**
* A function that checks whether the
* new cell is similar to the one
* previously used. Then, a significant
* amount of the data can be reused,
* e.g. the derivatives of the basis
* functions in real space, shape_grad.
*/
void
check_cell_similarity (const typename Triangulation<dim,spacedim>::cell_iterator &cell);
private:
/**
* Copy constructor. Since
* objects of this class are not
* copyable, we make it private,
* and also do not implement it.
*/
FEValuesBase (const FEValuesBase &);
/**
* Copy operator. Since
* objects of this class are not
* copyable, we make it private,
* and also do not implement it.
*/
FEValuesBase & operator= (const FEValuesBase &);
/**
* A cache for all possible FEValuesViews
* objects.
*/
internal::FEValuesViews::Cache<dim,spacedim> fe_values_views_cache;
/**
* Make the view classes friends of this
* class, since they access internal
* data.
*/
template <int, int> friend class FEValuesViews::Scalar;
template <int, int> friend class FEValuesViews::Vector;
template <int, int, int> friend class FEValuesViews::SymmetricTensor;
};
/**
* Finite element evaluated in quadrature points of a cell.
*
* This function implements the initialization routines for
* FEValuesBase, if values in quadrature points of a cell are
* needed. For further documentation see this class.
*
* @author Wolfgang Bangerth, 1998, Guido Kanschat, 2001
*/
template <int dim, int spacedim=dim>
class FEValues : public FEValuesBase<dim,spacedim>
{
public:
/**
* Dimension of the object over
* which we integrate. For the
* present class, this is equal
* to <code>dim</code>.
*/
static const unsigned int integral_dimension = dim;
/**
* Constructor. Gets cell
* independent data from mapping
* and finite element objects,
* matching the quadrature rule
* and update flags.
*/
FEValues (const Mapping<dim,spacedim> &mapping,
const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim> &quadrature,
const UpdateFlags update_flags);
/**
* Constructor. Uses MappingQ1
* implicitly.
*/
FEValues (const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim> &quadrature,
const UpdateFlags update_flags);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a DoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this FEValues
* object.
*/
void reinit (const typename DoFHandler<dim,spacedim>::cell_iterator &cell);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a hp::DoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this @p FEValues
* object.
*/
void reinit (const typename hp::DoFHandler<dim,spacedim>::cell_iterator &cell);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a MGDoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this FEValues
* object.
*/
void reinit (const typename MGDoFHandler<dim,spacedim>::cell_iterator &cell);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a Triangulation
* object", and the given finite
* element. Since iterators into
* triangulation alone only
* convey information about the
* geometry of a cell, but not
* about degrees of freedom
* possibly associated with this
* cell, you will not be able to
* call some functions of this
* class if they need information
* about degrees of
* freedom. These functions are,
* above all, the
* <tt>get_function_value/gradients/hessians/laplacians</tt>
* functions. If you want to call
* these functions, you have to
* call the @p reinit variants
* that take iterators into
* DoFHandler or other DoF
* handler type objects.
*/
void reinit (const typename Triangulation<dim,spacedim>::cell_iterator &cell);
/**
* Return a reference to the copy
* of the quadrature formula
* stored by this object.
*/
const Quadrature<dim> & get_quadrature () const;
/**
* Determine an estimate for the
* memory consumption (in bytes)
* of this object.
*/
unsigned int memory_consumption () const;
/**
* Return a reference to this
* very object.
*
* Though it seems that it is not very
* useful, this function is there to
* provide capability to the hpFEValues
* class, in which case it provides the
* FEValues object for the present cell
* (remember that for hp finite elements,
* the actual FE object used may change
* from cell to cell, so we also need
* different FEValues objects for
* different cells; once you reinitialize
* the hpFEValues object for a specific
* cell, it retrieves the FEValues object
* for the FE on that cell and returns it
* through a function of the same name as
* this one; this function here therefore
* only provides the same interface so
* that one can templatize on
* FEValues/hpFEValues).
*/
const FEValues<dim,spacedim> & get_present_fe_values () const;
private:
/**
* Store a copy of the quadrature
* formula here.
*/
const Quadrature<dim> quadrature;
/**
* Do work common to the two
* constructors.
*/
void initialize (const UpdateFlags update_flags);
/**
* The reinit() functions do
* only that part of the work
* that requires knowledge of the
* type of iterator. After
* setting present_cell(),
* they pass on to this function,
* which does the real work, and
* which is independent of the
* actual type of the cell
* iterator.
*/
void do_reinit ();
};
/**
* Extend the interface of FEValuesBase to values that only make sense
* when evaluating something on the surface of a cell. All the data
* that is available in the interior of cells is also available here.
*
* On surfaces of mesh cells, boundary forms are
* additional values that can be computed. This class provides the
* interface to access those. Implementations are in derived classes
* FEFaceValues and FESubfaceValues.
*
* The boundary form is the cross product of the images of the unit
* tangential vectors. Therefore, it is the unit normal vector
* multiplied with the surface element. Since it may be cheaper to
* compute the boundary form immediately, use this value to integrate
* <tt>n.ds</tt>.
*
* See FEValuesBase
*
* @author Wolfgang Bangerth, 1998, Guido Kanschat, 2000, 2001
*/
template <int dim, int spacedim=dim>
class FEFaceValuesBase : public FEValuesBase<dim,spacedim>
{
public:
/**
* Dimension of the object over
* which we integrate. For the
* present class, this is equal
* to <code>dim-1</code>.
*/
static const unsigned int integral_dimension = dim-1;
/**
* Constructor. Call the constructor of
* the base class and set up the arrays
* of this class with the right sizes.
* Actually filling these arrays is a
* duty of the derived class's
* constructors.
*
* @p n_faces_or_subfaces is the number
* of faces or subfaces that this object
* is to store. The actual number depends
* on the derived class, for
* FEFaceValues it is <tt>2*dim</tt>, while for
* the FESubfaceValues class it is
* <tt>2*dim*(1<<(dim-1))</tt>, i.e. the number
* of faces times the number of subfaces
* per face.
*/
FEFaceValuesBase (const unsigned int n_q_points,
const unsigned int dofs_per_cell,
const UpdateFlags update_flags,
const Mapping<dim,spacedim> &mapping,
const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim-1>& quadrature);
/**
* Boundary form of the
* transformation of the cell at
* the <tt>i</tt>th quadrature point.
*
* The boundary form is the cross
* product of the images of the
* unit tangential
* vectors. Therefore, it is the
* unit normal vector multiplied
* with the surface
* element. Since it may be
* cheaper to compute the
* boundary form immediately, use
* this value to integrate
* <tt>n.ds</tt>.
*/
const Tensor<1,spacedim> & boundary_form (const unsigned int i) const;
/**
* Return the list of outward
* normal vectors times the
* Jacobian of the surface
* mapping.
*/
const std::vector<Tensor<1,spacedim> > & get_boundary_forms () const;
/**
* Return the index of the face
* selected the last time the
* reinit() function was called.
*/
unsigned int get_face_index() const;
/**
* Return a reference to the copy
* of the quadrature formula
* stored by this object.
*/
const Quadrature<dim-1> & get_quadrature () const;
/**
* Determine an estimate for the
* memory consumption (in bytes)
* of this object.
*/
unsigned int memory_consumption () const;
protected:
/**
* Index of the face selected the
* last time the reinit()
* function was called.
*/
unsigned int present_face_index;
/**
* Store a copy of the quadrature
* formula here.
*/
const Quadrature<dim-1> quadrature;
};
/**
* Finite element evaluated in quadrature points on a face.
*
* This class adds the functionality of FEFaceValuesBase to
* FEValues; see there for more documentation.
*
* Since finite element functions and their derivatives may be
* discontinuous at cell boundaries, there is no restriction of this
* function to a mesh face. But, there are limits of these values
* approaching the face from either of the neighboring cells.
*
* @author Wolfgang Bangerth, 1998, Guido Kanschat, 2000, 2001
*/
template <int dim, int spacedim=dim>
class FEFaceValues : public FEFaceValuesBase<dim,spacedim>
{
public:
/**
* Dimension in which this object
* operates.
*/
static const unsigned int dimension = dim;
static const unsigned int space_dimension = spacedim;
/**
* Dimension of the object over
* which we integrate. For the
* present class, this is equal
* to <code>dim-1</code>.
*/
static const unsigned int integral_dimension = dim-1;
/**
* Constructor. Gets cell
* independent data from mapping
* and finite element objects,
* matching the quadrature rule
* and update flags.
*/
FEFaceValues (const Mapping<dim,spacedim> &mapping,
const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim-1> &quadrature,
const UpdateFlags update_flags);
/**
* Constructor. Uses MappingQ1
* implicitly.
*/
FEFaceValues (const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim-1> &quadrature,
const UpdateFlags update_flags);
/**
* Reinitialize the gradients, Jacobi
* determinants, etc for the face with
* number @p face_no of @p cell
* and the given finite element.
*/
void reinit (const typename DoFHandler<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a hp::DoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this FEValues
* object.
*/
void reinit (const typename hp::DoFHandler<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a MGDoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this FEValues
* object.
*/
void reinit (const typename MGDoFHandler<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given face on given cell
* of type "iterator into a
* Triangulation object", and the
* given finite element. Since
* iterators into triangulation
* alone only convey information
* about the geometry of a cell,
* but not about degrees of
* freedom possibly associated
* with this cell, you will not
* be able to call some functions
* of this class if they need
* information about degrees of
* freedom. These functions are,
* above all, the
* <tt>get_function_value/gradients/hessians</tt>
* functions. If you want to call
* these functions, you have to
* call the @p reinit variants
* that take iterators into
* DoFHandler or other DoF
* handler type objects.
*/
void reinit (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no);
/**
* Return a reference to this
* very object.
*
* Though it seems that it is not very
* useful, this function is there to
* provide capability to the hpFEValues
* class, in which case it provides the
* FEValues object for the present cell
* (remember that for hp finite elements,
* the actual FE object used may change
* from cell to cell, so we also need
* different FEValues objects for
* different cells; once you reinitialize
* the hpFEValues object for a specific
* cell, it retrieves the FEValues object
* for the FE on that cell and returns it
* through a function of the same name as
* this one; this function here therefore
* only provides the same interface so
* that one can templatize on
* FEValues/hpFEValues).
*/
const FEFaceValues<dim,spacedim> & get_present_fe_values () const;
private:
/**
* Do work common to the two
* constructors.
*/
void initialize (const UpdateFlags update_flags);
/**
* The reinit() functions do
* only that part of the work
* that requires knowledge of the
* type of iterator. After
* setting present_cell(),
* they pass on to this function,
* which does the real work, and
* which is independent of the
* actual type of the cell
* iterator.
*/
void do_reinit (const unsigned int face_no);
};
/**
* Finite element evaluated in quadrature points on a face.
*
* This class adds the functionality of FEFaceValuesBase to
* FEValues; see there for more documentation.
*
* This class is used for faces lying on a refinement edge. In this
* case, the neighboring cell is refined. To be able to compute
* differences between interior and exterior function values, the
* refinement of the neighboring cell must be simulated on this
* cell. This is achieved by applying a quadrature rule that simulates
* the refinement. The resulting data fields are split up to reflect
* the refinement structure of the neighbor: a subface number
* corresponds to the number of the child of the neighboring face.
*
* @author Wolfgang Bangerth, 1998, Guido Kanschat, 2000, 2001
*/
template <int dim, int spacedim=dim>
class FESubfaceValues : public FEFaceValuesBase<dim,spacedim>
{
public:
/**
* Dimension in which this object
* operates.
*/
static const unsigned int dimension = dim;
/**
* Dimension of the space in
* which this object operates.
*/
static const unsigned int space_dimension = spacedim;
/**
* Dimension of the object over
* which we integrate. For the
* present class, this is equal
* to <code>dim-1</code>.
*/
static const unsigned int integral_dimension = dim-1;
/**
* Constructor. Gets cell
* independent data from mapping
* and finite element objects,
* matching the quadrature rule
* and update flags.
*/
FESubfaceValues (const Mapping<dim,spacedim> &mapping,
const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim-1> &face_quadrature,
const UpdateFlags update_flags);
/**
* Constructor. Uses MappingQ1
* implicitly.
*/
FESubfaceValues (const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim-1> &face_quadrature,
const UpdateFlags update_flags);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a DoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this
* FESubfaceValues object.
*/
void reinit (const typename DoFHandler<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int subface_no);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a hp::DoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this FEValues
* object.
*/
void reinit (const typename hp::DoFHandler<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int subface_no);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given cell of type
* "iterator into a MGDoFHandler
* object", and the finite
* element associated with this
* object. It is assumed that the
* finite element used by the
* given cell is also the one
* used by this FEValues
* object.
*/
void reinit (const typename MGDoFHandler<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int subface_no);
/**
* Reinitialize the gradients,
* Jacobi determinants, etc for
* the given subface on given
* cell of type "iterator into a
* Triangulation object", and the
* given finite element. Since
* iterators into triangulation
* alone only convey information
* about the geometry of a cell,
* but not about degrees of
* freedom possibly associated
* with this cell, you will not
* be able to call some functions
* of this class if they need
* information about degrees of
* freedom. These functions are,
* above all, the
* <tt>get_function_value/gradients/hessians</tt>
* functions. If you want to call
* these functions, you have to
* call the @p reinit variants
* that take iterators into
* DoFHandler or other DoF
* handler type objects.
*/
void reinit (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int subface_no);
/**
* Return a reference to this
* very object.
*
* Though it seems that it is not very
* useful, this function is there to
* provide capability to the hpFEValues
* class, in which case it provides the
* FEValues object for the present cell
* (remember that for hp finite elements,
* the actual FE object used may change
* from cell to cell, so we also need
* different FEValues objects for
* different cells; once you reinitialize
* the hpFEValues object for a specific
* cell, it retrieves the FEValues object
* for the FE on that cell and returns it
* through a function of the same name as
* this one; this function here therefore
* only provides the same interface so
* that one can templatize on
* FEValues/hpFEValues).
*/
const FESubfaceValues<dim,spacedim> & get_present_fe_values () const;
/**
* @todo Document this
*
* @ingroup Exceptions
*/
DeclException0 (ExcReinitCalledWithBoundaryFace);
/**
* @todo Document this
*
* @ingroup Exceptions
*/
DeclException0 (ExcFaceHasNoSubfaces);
private:
/**
* Do work common to the two
* constructors.
*/
void initialize (const UpdateFlags update_flags);
/**
* The reinit() functions do
* only that part of the work
* that requires knowledge of the
* type of iterator. After
* setting present_cell(),
* they pass on to this function,
* which does the real work, and
* which is independent of the
* actual type of the cell
* iterator.
*/
void do_reinit (const unsigned int face_no,
const unsigned int subface_no);
};
/*@}*/
#ifndef DOXYGEN
/*------------------------ Inline functions: namespace FEValuesExtractors --------*/
namespace FEValuesExtractors
{
inline
Scalar::Scalar (const unsigned int component)
:
component (component)
{}
inline
Vector::Vector (const unsigned int first_vector_component)
:
first_vector_component (first_vector_component)
{}
template <int rank>
inline
SymmetricTensor<rank>::SymmetricTensor (const unsigned int first_tensor_component)
:
first_tensor_component (first_tensor_component)
{}
}
/*------------------------ Inline functions: namespace FEValuesViews --------*/
namespace FEValuesViews
{
template <int dim, int spacedim>
inline
typename Scalar<dim,spacedim>::value_type
Scalar<dim,spacedim>::value (const unsigned int shape_function,
const unsigned int q_point) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_values,
typename FVB::ExcAccessToUninitializedField());
// an adaptation of the
// FEValuesBase::shape_value_component
// function except that here we know the
// component as fixed and we have
// pre-computed and cached a bunch of
// information. see the comments there
if (shape_function_data[shape_function].is_nonzero_shape_function_component)
return fe_values.shape_values(shape_function_data[shape_function]
.row_index,
q_point);
else
return 0;
}
template <int dim, int spacedim>
inline
typename Scalar<dim,spacedim>::gradient_type
Scalar<dim,spacedim>::gradient (const unsigned int shape_function,
const unsigned int q_point) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_gradients,
typename FVB::ExcAccessToUninitializedField());
// an adaptation of the
// FEValuesBase::shape_grad_component
// function except that here we know the
// component as fixed and we have
// pre-computed and cached a bunch of
// information. see the comments there
if (shape_function_data[shape_function].is_nonzero_shape_function_component)
return fe_values.shape_gradients[shape_function_data[shape_function]
.row_index][q_point];
else
return gradient_type();
}
template <int dim, int spacedim>
inline
typename Scalar<dim,spacedim>::hessian_type
Scalar<dim,spacedim>::hessian (const unsigned int shape_function,
const unsigned int q_point) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_hessians,
typename FVB::ExcAccessToUninitializedField());
// an adaptation of the
// FEValuesBase::shape_grad_component
// function except that here we know the
// component as fixed and we have
// pre-computed and cached a bunch of
// information. see the comments there
if (shape_function_data[shape_function].is_nonzero_shape_function_component)
return fe_values.shape_hessians[shape_function_data[shape_function].row_index][q_point];
else
return hessian_type();
}
template <int dim, int spacedim>
inline
typename Vector<dim,spacedim>::value_type
Vector<dim,spacedim>::value (const unsigned int shape_function,
const unsigned int q_point) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_values,
typename FVB::ExcAccessToUninitializedField());
// same as for the scalar case except
// that we have one more index
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
return value_type();
else if (snc != -1)
{
value_type return_value;
return_value[shape_function_data[shape_function].single_nonzero_component_index]
= fe_values.shape_values(snc,q_point);
return return_value;
}
else
{
value_type return_value;
for (unsigned int d=0; d<dim; ++d)
if (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
return_value[d]
= fe_values.shape_values(shape_function_data[shape_function].row_index[d],q_point);
return return_value;
}
}
template <int dim, int spacedim>
inline
typename Vector<dim,spacedim>::gradient_type
Vector<dim,spacedim>::gradient (const unsigned int shape_function,
const unsigned int q_point) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_gradients,
typename FVB::ExcAccessToUninitializedField());
// same as for the scalar case except
// that we have one more index
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
return gradient_type();
else if (snc != -1)
{
gradient_type return_value;
return_value[shape_function_data[shape_function].single_nonzero_component_index]
= fe_values.shape_gradients[snc][q_point];
return return_value;
}
else
{
gradient_type return_value;
for (unsigned int d=0; d<dim; ++d)
if (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
return_value[d]
= fe_values.shape_gradients[shape_function_data[shape_function].row_index[d]][q_point];
return return_value;
}
}
template <int dim, int spacedim>
inline
typename Vector<dim,spacedim>::divergence_type
Vector<dim,spacedim>::divergence (const unsigned int shape_function,
const unsigned int q_point) const
{
// this function works like in
// the case above
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_gradients,
typename FVB::ExcAccessToUninitializedField());
// same as for the scalar case except
// that we have one more index
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
return divergence_type();
else if (snc != -1)
return
fe_values.shape_gradients[snc][q_point][shape_function_data[shape_function].single_nonzero_component_index];
else
{
divergence_type return_value = 0;
for (unsigned int d=0; d<dim; ++d)
if (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
return_value
+= fe_values.shape_gradients[shape_function_data[shape_function].row_index[d]][q_point][d];
return return_value;
}
}
template <int dim, int spacedim>
inline
typename Vector<dim,spacedim>::curl_type
Vector<dim,spacedim>::curl (const unsigned int shape_function, const unsigned int q_point) const {
// this function works like in the case above
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_gradients,
typename FVB::ExcAccessToUninitializedField());
// same as for the scalar case except that we have one more index
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
return curl_type ();
else
switch (dim) {
case 1: {
Assert (false, ExcMessage("Computing the curl in 1d is not a useful operation"));
return curl_type ();
}
case 2: {
if (snc != -1) {
curl_type return_value;
switch (shape_function_data[shape_function].single_nonzero_component_index) {
case 0: {
return_value[0] = -1.0 * fe_values.shape_gradients[snc][q_point][1];
return return_value;
}
default: {
return_value[0] = fe_values.shape_gradients[snc][q_point][2];
return return_value;
}
}
}
else {
curl_type return_value;
return_value[0] = 0.0;
if (shape_function_data[shape_function].is_nonzero_shape_function_component[0])
return_value[0]
-= fe_values.shape_gradients[shape_function_data[shape_function].row_index[0]][q_point][1];
if (shape_function_data[shape_function].is_nonzero_shape_function_component[1])
return_value[0]
+= fe_values.shape_gradients[shape_function_data[shape_function].row_index[1]][q_point][0];
return return_value;
}
}
case 3: {
if (snc != -1) {
curl_type return_value;
switch (shape_function_data[shape_function].single_nonzero_component_index) {
case 0: {
return_value[0] = 0;
return_value[1] = fe_values.shape_gradients[snc][q_point][2];
return_value[2] = -1.0 * fe_values.shape_gradients[snc][q_point][1];
return return_value;
}
case 1: {
return_value[0] = -1.0 * fe_values.shape_gradients[snc][q_point][2];
return_value[1] = 0;
return_value[2] = fe_values.shape_gradients[snc][q_point][0];
return return_value;
}
default: {
return_value[0] = fe_values.shape_gradients[snc][q_point][1];
return_value[1] = -1.0 * fe_values.shape_gradients[snc][q_point][0];
return_value[2] = 0;
return return_value;
}
}
}
else {
curl_type return_value;
for (unsigned int i = 0; i < dim; ++i)
return_value[i] = 0.0;
if (shape_function_data[shape_function].is_nonzero_shape_function_component[0]) {
return_value[1]
+= fe_values.shape_gradients[shape_function_data[shape_function].row_index[0]][q_point][2];
return_value[2]
-= fe_values.shape_gradients[shape_function_data[shape_function].row_index[0]][q_point][1];
}
if (shape_function_data[shape_function].is_nonzero_shape_function_component[1]) {
return_value[0]
-= fe_values.shape_gradients[shape_function_data[shape_function].row_index[1]][q_point][2];
return_value[2]
+= fe_values.shape_gradients[shape_function_data[shape_function].row_index[1]][q_point][0];
}
if (shape_function_data[shape_function].is_nonzero_shape_function_component[2]) {
return_value[0]
+= fe_values.shape_gradients[shape_function_data[shape_function].row_index[2]][q_point][1];
return_value[1]
-= fe_values.shape_gradients[shape_function_data[shape_function].row_index[2]][q_point][0];
}
return return_value;
}
}
}
}
template <int dim, int spacedim>
inline
typename Vector<dim,spacedim>::hessian_type
Vector<dim,spacedim>::hessian (const unsigned int shape_function,
const unsigned int q_point) const
{
// this function works like in
// the case above
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_hessians,
typename FVB::ExcAccessToUninitializedField());
// same as for the scalar case except
// that we have one more index
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
return hessian_type();
else if (snc != -1)
{
hessian_type return_value;
return_value[shape_function_data[shape_function].single_nonzero_component_index]
= fe_values.shape_hessians[snc][q_point];
return return_value;
}
else
{
hessian_type return_value;
for (unsigned int d=0; d<dim; ++d)
if (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
return_value[d]
= fe_values.shape_hessians[shape_function_data[shape_function].row_index[d]][q_point];
return return_value;
}
}
namespace
{
/**
* Return the symmetrized version of a
* tensor whose n'th row equals the
* second argument, with all other rows
* equal to zero.
*/
inline
dealii::SymmetricTensor<2,1>
symmetrize_single_row (const unsigned int n,
const Tensor<1,1> &t)
{
Assert (n < 1, ExcIndexRange (n, 0, 1));
const double array[1] = { t[0] };
return dealii::SymmetricTensor<2,1>(array);
}
inline
dealii::SymmetricTensor<2,2>
symmetrize_single_row (const unsigned int n,
const Tensor<1,2> &t)
{
switch (n)
{
case 0:
{
const double array[3] = { t[0], 0, t[1]/2 };
return dealii::SymmetricTensor<2,2>(array);
}
case 1:
{
const double array[3] = { 0, t[1], t[0]/2 };
return dealii::SymmetricTensor<2,2>(array);
}
default:
{
Assert (false, ExcIndexRange (n, 0, 2));
return dealii::SymmetricTensor<2,2>();
}
}
}
inline
dealii::SymmetricTensor<2,3>
symmetrize_single_row (const unsigned int n,
const Tensor<1,3> &t)
{
switch (n)
{
case 0:
{
const double array[6] = { t[0], 0, 0, t[1]/2, t[2]/2, 0 };
return dealii::SymmetricTensor<2,3>(array);
}
case 1:
{
const double array[6] = { 0, t[1], 0, t[0]/2, 0, t[2]/2 };
return dealii::SymmetricTensor<2,3>(array);
}
case 2:
{
const double array[6] = { 0, 0, t[2], 0, t[0]/2, t[1]/2 };
return dealii::SymmetricTensor<2,3>(array);
}
default:
{
Assert (false, ExcIndexRange (n, 0, 3));
return dealii::SymmetricTensor<2,3>();
}
}
}
}
template <int dim, int spacedim>
inline
typename Vector<dim,spacedim>::symmetric_gradient_type
Vector<dim,spacedim>::symmetric_gradient (const unsigned int shape_function,
const unsigned int q_point) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (shape_function < fe_values.fe->dofs_per_cell,
ExcIndexRange (shape_function, 0, fe_values.fe->dofs_per_cell));
Assert (fe_values.update_flags & update_gradients,
typename FVB::ExcAccessToUninitializedField());
// same as for the scalar case except
// that we have one more index
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
return symmetric_gradient_type();
else if (snc != -1)
return symmetrize_single_row (shape_function_data[shape_function].single_nonzero_component_index,
fe_values.shape_gradients[snc][q_point]);
else
{
gradient_type return_value;
for (unsigned int d=0; d<dim; ++d)
if (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
return_value[d]
= fe_values.shape_gradients[shape_function_data[shape_function].row_index[d]][q_point];
return symmetrize(return_value);
}
}
}
/*------------------------ Inline functions: FEValuesBase ------------------------*/
template <int dim, int spacedim>
inline
const FEValuesViews::Scalar<dim,spacedim> &
FEValuesBase<dim,spacedim>::
operator[] (const FEValuesExtractors::Scalar &scalar) const
{
Assert (scalar.component < fe_values_views_cache.scalars.size(),
ExcIndexRange (scalar.component,
0, fe_values_views_cache.scalars.size()));
return fe_values_views_cache.scalars[scalar.component];
}
template <int dim, int spacedim>
inline
const FEValuesViews::Vector<dim,spacedim> &
FEValuesBase<dim,spacedim>::
operator[] (const FEValuesExtractors::Vector &vector) const
{
Assert (vector.first_vector_component <
fe_values_views_cache.vectors.size(),
ExcIndexRange (vector.first_vector_component,
0, fe_values_views_cache.vectors.size()));
return fe_values_views_cache.vectors[vector.first_vector_component];
}
template <int dim, int spacedim>
inline
const FEValuesViews::SymmetricTensor<2,dim,spacedim> &
FEValuesBase<dim,spacedim>::
operator[] (const FEValuesExtractors::SymmetricTensor<2> &tensor) const
{
Assert (tensor.first_tensor_component <
fe_values_views_cache.symmetric_second_order_tensors.size(),
ExcIndexRange (tensor.first_tensor_component,
0, fe_values_views_cache.symmetric_second_order_tensors.size()));
return fe_values_views_cache.symmetric_second_order_tensors[tensor.first_tensor_component];
}
template <int dim, int spacedim>
inline
const double &
FEValuesBase<dim,spacedim>::shape_value (const unsigned int i,
const unsigned int j) const
{
Assert (i < fe->dofs_per_cell,
ExcIndexRange (i, 0, fe->dofs_per_cell));
Assert (this->update_flags & update_values,
ExcAccessToUninitializedField());
Assert (fe->is_primitive (i),
ExcShapeFunctionNotPrimitive(i));
// if the entire FE is primitive,
// then we can take a short-cut:
if (fe->is_primitive())
return this->shape_values(i,j);
else
// otherwise, use the mapping
// between shape function numbers
// and rows. note that by the
// assertions above, we know that
// this particular shape function
// is primitive, so there is no
// question to which vector
// component the call of this
// function refers
return this->shape_values(this->shape_function_to_row_table[i], j);
}
template <int dim, int spacedim>
inline
double
FEValuesBase<dim,spacedim>::shape_value_component (const unsigned int i,
const unsigned int j,
const unsigned int component) const
{
Assert (i < fe->dofs_per_cell,
ExcIndexRange (i, 0, fe->dofs_per_cell));
Assert (this->update_flags & update_values,
ExcAccessToUninitializedField());
Assert (component < fe->n_components(),
ExcIndexRange(component, 0, fe->n_components()));
// if this particular shape
// function is primitive, then we
// can take a short-cut by checking
// whether the requested component
// is the only non-zero one (note
// that calling
// system_to_component_table only
// works if the shape function is
// primitive):
if (fe->is_primitive(i))
{
if (component == fe->system_to_component_index(i).first)
return this->shape_values(this->shape_function_to_row_table[i],j);
else
return 0;
}
else
{
// no, this shape function is
// not primitive. then we have
// to loop over its components
// to find the corresponding
// row in the arrays of this
// object. before that check
// whether the shape function
// is non-zero at all within
// this component:
if (fe->get_nonzero_components(i)[component] == false)
return 0;
// count how many non-zero
// component the shape function
// has before the one we are
// looking for, and add this to
// the offset of the first
// non-zero component of this
// shape function in the arrays
// we index presently:
const unsigned int
row = (this->shape_function_to_row_table[i]
+
std::count (fe->get_nonzero_components(i).begin(),
fe->get_nonzero_components(i).begin()+component,
true));
return this->shape_values(row, j);
}
}
template <int dim, int spacedim>
inline
const Tensor<1,spacedim> &
FEValuesBase<dim,spacedim>::shape_grad (const unsigned int i,
const unsigned int j) const
{
Assert (i < fe->dofs_per_cell,
ExcIndexRange (i, 0, fe->dofs_per_cell));
Assert (this->update_flags & update_gradients,
ExcAccessToUninitializedField());
Assert (fe->is_primitive (i),
ExcShapeFunctionNotPrimitive(i));
Assert (i<this->shape_gradients.size(),
ExcIndexRange (i, 0, this->shape_gradients.size()));
Assert (j<this->shape_gradients[0].size(),
ExcIndexRange (j, 0, this->shape_gradients[0].size()));
// if the entire FE is primitive,
// then we can take a short-cut:
if (fe->is_primitive())
return this->shape_gradients[i][j];
else
// otherwise, use the mapping
// between shape function numbers
// and rows. note that by the
// assertions above, we know that
// this particular shape function
// is primitive, so there is no
// question to which vector
// component the call of this
// function refers
return this->shape_gradients[this->shape_function_to_row_table[i]][j];
}
template <int dim, int spacedim>
inline
Tensor<1,spacedim>
FEValuesBase<dim,spacedim>::shape_grad_component (const unsigned int i,
const unsigned int j,
const unsigned int component) const
{
Assert (i < fe->dofs_per_cell,
ExcIndexRange (i, 0, fe->dofs_per_cell));
Assert (this->update_flags & update_gradients,
ExcAccessToUninitializedField());
Assert (component < fe->n_components(),
ExcIndexRange(component, 0, fe->n_components()));
// if this particular shape
// function is primitive, then we
// can take a short-cut by checking
// whether the requested component
// is the only non-zero one (note
// that calling
// system_to_component_table only
// works if the shape function is
// primitive):
if (fe->is_primitive(i))
{
if (component == fe->system_to_component_index(i).first)
return this->shape_gradients[this->shape_function_to_row_table[i]][j];
else
return Tensor<1,spacedim>();
}
else
{
// no, this shape function is
// not primitive. then we have
// to loop over its components
// to find the corresponding
// row in the arrays of this
// object. before that check
// whether the shape function
// is non-zero at all within
// this component:
if (fe->get_nonzero_components(i)[component] == false)
return Tensor<1,spacedim>();
// count how many non-zero
// component the shape function
// has before the one we are
// looking for, and add this to
// the offset of the first
// non-zero component of this
// shape function in the arrays
// we index presently:
const unsigned int
row = (this->shape_function_to_row_table[i]
+
std::count (fe->get_nonzero_components(i).begin(),
fe->get_nonzero_components(i).begin()+component,
true));
return this->shape_gradients[row][j];
}
}
template <int dim, int spacedim>
inline
const Tensor<2,spacedim> &
FEValuesBase<dim,spacedim>::shape_hessian (const unsigned int i,
const unsigned int j) const
{
Assert (i < fe->dofs_per_cell,
ExcIndexRange (i, 0, fe->dofs_per_cell));
Assert (this->update_flags & update_hessians,
ExcAccessToUninitializedField());
Assert (fe->is_primitive (i),
ExcShapeFunctionNotPrimitive(i));
Assert (i<this->shape_hessians.size(),
ExcIndexRange (i, 0, this->shape_hessians.size()));
Assert (j<this->shape_hessians[0].size(),
ExcIndexRange (j, 0, this->shape_hessians[0].size()));
// if the entire FE is primitive,
// then we can take a short-cut:
if (fe->is_primitive())
return this->shape_hessians[i][j];
else
// otherwise, use the mapping
// between shape function numbers
// and rows. note that by the
// assertions above, we know that
// this particular shape function
// is primitive, so there is no
// question to which vector
// component the call of this
// function refers
return this->shape_hessians[this->shape_function_to_row_table[i]][j];
}
template <int dim, int spacedim>
inline
const Tensor<2,spacedim> &
FEValuesBase<dim,spacedim>::shape_2nd_derivative (const unsigned int i,
const unsigned int j) const
{
return shape_hessian(i,j);
}
template <int dim, int spacedim>
inline
Tensor<2,spacedim>
FEValuesBase<dim,spacedim>::shape_hessian_component (const unsigned int i,
const unsigned int j,
const unsigned int component) const
{
Assert (i < fe->dofs_per_cell,
ExcIndexRange (i, 0, fe->dofs_per_cell));
Assert (this->update_flags & update_hessians,
ExcAccessToUninitializedField());
Assert (component < fe->n_components(),
ExcIndexRange(component, 0, fe->n_components()));
// if this particular shape
// function is primitive, then we
// can take a short-cut by checking
// whether the requested component
// is the only non-zero one (note
// that calling
// system_to_component_table only
// works if the shape function is
// primitive):
if (fe->is_primitive(i))
{
if (component == fe->system_to_component_index(i).first)
return this->shape_hessians[this->shape_function_to_row_table[i]][j];
else
return Tensor<2,spacedim>();
}
else
{
// no, this shape function is
// not primitive. then we have
// to loop over its components
// to find the corresponding
// row in the arrays of this
// object. before that check
// whether the shape function
// is non-zero at all within
// this component:
if (fe->get_nonzero_components(i)[component] == false)
return Tensor<2,spacedim>();
// count how many non-zero
// component the shape function
// has before the one we are
// looking for, and add this to
// the offset of the first
// non-zero component of this
// shape function in the arrays
// we index presently:
const unsigned int
row = (this->shape_function_to_row_table[i]
+
std::count (fe->get_nonzero_components(i).begin(),
fe->get_nonzero_components(i).begin()+component,
true));
return this->shape_hessians[row][j];
}
}
template <int dim, int spacedim>
inline
Tensor<2,spacedim>
FEValuesBase<dim,spacedim>::shape_2nd_derivative_component (const unsigned int i,
const unsigned int j,
const unsigned int component) const
{
return shape_hessian_component(i,j,component);
}
template <int dim, int spacedim>
inline
const FiniteElement<dim,spacedim> &
FEValuesBase<dim,spacedim>::get_fe () const
{
return *fe;
}
template <int dim, int spacedim>
inline
const Mapping<dim,spacedim> &
FEValuesBase<dim,spacedim>::get_mapping () const
{
return *mapping;
}
template <int dim, int spacedim>
inline
UpdateFlags
FEValuesBase<dim,spacedim>::get_update_flags () const
{
return this->update_flags;
}
template <int dim, int spacedim>
inline
const std::vector<Point<spacedim> > &
FEValuesBase<dim,spacedim>::get_quadrature_points () const
{
Assert (this->update_flags & update_quadrature_points, ExcAccessToUninitializedField());
return this->quadrature_points;
}
template <int dim, int spacedim>
inline
const std::vector<double> &
FEValuesBase<dim,spacedim>::get_JxW_values () const
{
Assert (this->update_flags & update_JxW_values, ExcAccessToUninitializedField());
return this->JxW_values;
}
template <int dim, int spacedim>
inline
const std::vector<Tensor<2,spacedim> >&
FEValuesBase<dim,spacedim>::get_jacobians () const
{
Assert (this->update_flags & update_jacobians, ExcAccessToUninitializedField());
return this->jacobians;
}
template <int dim, int spacedim>
inline
const std::vector<Tensor<3,spacedim> >&
FEValuesBase<dim,spacedim>::get_jacobian_grads () const
{
Assert (this->update_flags & update_jacobian_grads, ExcAccessToUninitializedField());
return this->jacobian_grads;
}
template <int dim, int spacedim>
inline
const std::vector<Tensor<2,spacedim> >&
FEValuesBase<dim,spacedim>::get_inverse_jacobians () const
{
Assert (this->update_flags & update_inverse_jacobians, ExcAccessToUninitializedField());
return this->inverse_jacobians;
}
template <int dim, int spacedim>
const Point<spacedim> &
FEValuesBase<dim,spacedim>::quadrature_point (const unsigned int i) const
{
Assert (this->update_flags & update_quadrature_points, ExcAccessToUninitializedField());
Assert (i<this->quadrature_points.size(), ExcIndexRange(i, 0, this->quadrature_points.size()));
return this->quadrature_points[i];
}
template <int dim, int spacedim>
inline
double
FEValuesBase<dim,spacedim>::JxW (const unsigned int i) const
{
Assert (this->update_flags & update_JxW_values, ExcAccessToUninitializedField());
Assert (i<this->JxW_values.size(), ExcIndexRange(i, 0, this->JxW_values.size()));
return this->JxW_values[i];
}
template <int dim, int spacedim>
inline
const Tensor<2,spacedim> &
FEValuesBase<dim,spacedim>::jacobian (const unsigned int i) const
{
Assert (this->update_flags & update_jacobians, ExcAccessToUninitializedField());
Assert (i<this->jacobians.size(), ExcIndexRange(i, 0, this->jacobians.size()));
return this->jacobians[i];
}
template <int dim, int spacedim>
inline
const Tensor<3,spacedim> &
FEValuesBase<dim,spacedim>::jacobian_grad (const unsigned int i) const
{
Assert (this->update_flags & update_jacobian_grads, ExcAccessToUninitializedField());
Assert (i<this->jacobian_grads.size(), ExcIndexRange(i, 0, this->jacobian_grads.size()));
return this->jacobian_grads[i];
}
template <int dim, int spacedim>
inline
const Tensor<2,spacedim> &
FEValuesBase<dim,spacedim>::inverse_jacobian (const unsigned int i) const
{
Assert (this->update_flags & update_inverse_jacobians, ExcAccessToUninitializedField());
Assert (i<this->inverse_jacobians.size(), ExcIndexRange(i, 0, this->inverse_jacobians.size()));
return this->inverse_jacobians[i];
}
template <int dim, int spacedim>
template <class InputVector>
inline
void
FEValuesBase<dim,spacedim>::get_function_grads (const InputVector &fe_function,
std::vector<Tensor<1,spacedim> > &gradients) const
{
get_function_gradients(fe_function, gradients);
}
template <int dim, int spacedim>
template <class InputVector>
inline
void
FEValuesBase<dim,spacedim>::get_function_grads (
const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<Tensor<1,spacedim> > &values) const
{
get_function_gradients(fe_function, indices, values);
}
template <int dim, int spacedim>
template <class InputVector>
inline
void
FEValuesBase<dim,spacedim>::
get_function_grads (const InputVector &fe_function,
std::vector<std::vector<Tensor<1,spacedim> > > &gradients) const
{
get_function_gradients(fe_function, gradients);
}
template <int dim, int spacedim>
template <class InputVector>
inline
void
FEValuesBase<dim,spacedim>::get_function_grads (
const InputVector& fe_function,
const VectorSlice<const std::vector<unsigned int> >& indices,
std::vector<std::vector<Tensor<1,spacedim> > >& values,
bool q_points_fastest) const
{
get_function_gradients(fe_function, indices, values, q_points_fastest);
}
template <int dim, int spacedim>
template <class InputVector>
inline
void
FEValuesBase<dim,spacedim>::
get_function_2nd_derivatives (const InputVector &fe_function,
std::vector<Tensor<2,spacedim> > &hessians) const
{
get_function_hessians(fe_function, hessians);
}
template <int dim, int spacedim>
template <class InputVector>
inline
void
FEValuesBase<dim,spacedim>::
get_function_2nd_derivatives (const InputVector &fe_function,
std::vector<std::vector<Tensor<2,spacedim> > > &hessians,
bool quadrature_points_fastest) const
{
get_function_hessians(fe_function, hessians, quadrature_points_fastest);
}
template <int dim, int spacedim>
inline
const Point<spacedim> &
FEValuesBase<dim,spacedim>::normal_vector (const unsigned int i) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (this->update_flags & update_normal_vectors,
typename FVB::ExcAccessToUninitializedField());
Assert (i<this->normal_vectors.size(),
ExcIndexRange(i, 0, this->normal_vectors.size()));
return this->normal_vectors[i];
}
template <int dim, int spacedim>
inline
const Point<spacedim> &
FEValuesBase<dim,spacedim>::cell_normal_vector (const unsigned int i) const
{
return this->normal_vector(i);
}
/*------------------------ Inline functions: FEValues ----------------------------*/
template <int dim, int spacedim>
inline
const Quadrature<dim> &
FEValues<dim,spacedim>::get_quadrature () const
{
return quadrature;
}
template <int dim, int spacedim>
inline
const FEValues<dim,spacedim> &
FEValues<dim,spacedim>::get_present_fe_values () const
{
return *this;
}
/*------------------------ Inline functions: FEFaceValuesBase --------------------*/
template <int dim, int spacedim>
inline
unsigned int
FEFaceValuesBase<dim,spacedim>::get_face_index () const
{
return present_face_index;
}
/*------------------------ Inline functions: FE*FaceValues --------------------*/
template <int dim, int spacedim>
inline
const Quadrature<dim-1> &
FEFaceValuesBase<dim,spacedim>::get_quadrature () const
{
return quadrature;
}
template <int dim, int spacedim>
inline
const FEFaceValues<dim,spacedim> &
FEFaceValues<dim,spacedim>::get_present_fe_values () const
{
return *this;
}
template <int dim, int spacedim>
inline
const FESubfaceValues<dim,spacedim> &
FESubfaceValues<dim,spacedim>::get_present_fe_values () const
{
return *this;
}
template <int dim, int spacedim>
inline
const Tensor<1,spacedim> &
FEFaceValuesBase<dim,spacedim>::boundary_form (const unsigned int i) const
{
typedef FEValuesBase<dim,spacedim> FVB;
Assert (i<this->boundary_forms.size(),
ExcIndexRange(i, 0, this->boundary_forms.size()));
Assert (this->update_flags & update_boundary_forms,
typename FVB::ExcAccessToUninitializedField());
return this->boundary_forms[i];
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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