/usr/include/deal.II/fe/fe_values.h is in libdeal.ii-dev 8.1.0-6ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// $Id: fe_values.h 31932 2013-12-08 02:15:54Z heister $
//
// Copyright (C) 1998 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__fe_values_h
#define __deal2__fe_values_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/subscriptor.h>
#include <deal.II/base/point.h>
#include <deal.II/base/derivative_form.h>
#include <deal.II/base/symmetric_tensor.h>
#include <deal.II/base/vector_slice.h>
#include <deal.II/base/quadrature.h>
#include <deal.II/base/table.h>
#include <deal.II/grid/tria.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/hp/dof_handler.h>
#include <deal.II/fe/fe.h>
#include <deal.II/fe/fe_update_flags.h>
#include <deal.II/fe/fe_values_extractors.h>
#include <deal.II/fe/mapping.h>
#include <deal.II/multigrid/mg_dof_handler.h>
#include <algorithm>
#include <memory>
// dummy include in order to have the
// definition of PetscScalar available
// without including other PETSc stuff
#ifdef DEAL_II_WITH_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 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. You
* typically get objects of classes defined in this namespace by applying
* FEValuesExtractors objects to a FEValues, FEFaceValues or FESubfaceValues
* objects using the square bracket operator.
*
* 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.
*
* You get an object of this type if you apply a FEValuesExtractors::Scalar
* to an FEValues, FEFaceValues or FESubfaceValues object.
*
* @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 dealii::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 dealii::Tensor<2,spacedim> hessian_type;
/**
* 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;
};
/**
* 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.
*
* @param shape_function Number of the shape function to be
* evaluated. Note that this number runs from zero to dofs_per_cell, even
* in the case of an FEFaceValues or FESubfaceValues object.
*
* @param q_point Number of the quadrature point at which function is to
* be evaluated
*/
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.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* 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.
*
* 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.
*
* 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. 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;
/**
* Store the data about shape functions.
*/
std::vector<ShapeFunctionData> shape_function_data;
};
/**
* A class representing a view to a set of <code>spacedim</code> components
* forming a vector part of a vector-valued finite element. Views are
* discussed in the @ref vector_valued module.
*
* Note that in the current context, a vector is meant in the sense physics
* uses it: it has <code>spacedim</code> components that behave in specific
* ways under coordinate system transformations. Examples include velocity
* or displacement fields. This is opposed to how mathematics uses the word
* "vector" (and how we use this word in other contexts in the library, for
* example in the Vector class), where it really stands for a collection of
* numbers. An example of this latter use of the word could be the set of
* concentrations of chemical species in a flame; however, these are really
* just a collection of scalar variables, since they do not change if the
* coordinate system is rotated, unlike the components of a velocity vector,
* and consequently, this class should not be used for this context.
*
* This class allows to query the value, gradient and divergence of
* (components of) shape functions and solutions representing vectors. The
* gradient of a vector $d_{k}, 0\le k<\text{dim}$ is defined as $S_{ij} =
* \frac{\partial d_{i}}{\partial x_j}, 0\le i,j<\text{dim}$.
*
* You get an object of this type if you apply a FEValuesExtractors::Vector
* to an FEValues, FEFaceValues or FESubfaceValues object.
*
* @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 dealii::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>.
*
* See the general documentation of this class for how exactly the
* gradient of a vector is defined.
*/
typedef dealii::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>.
*
* The symmetric gradient of a vector field $\mathbf v$ is defined as
* $\varepsilon(\mathbf v)=\frac 12 (\nabla \mathbf v + \nabla \mathbf
* v^T)$.
*/
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 dealii::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 dealii::Tensor<3,spacedim> hessian_type;
/**
* 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[spacedim];
/**
* 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[spacedim];
/**
* 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;
};
/**
* 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.
*
* @param shape_function Number of the shape function to be
* evaluated. Note that this number runs from zero to dofs_per_cell, even
* in the case of an FEFaceValues or FESubfaceValues object.
*
* @param q_point Number of the quadrature point at which function is to
* be evaluated
*/
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.
*
* See the general documentation of this class for how exactly the
* gradient of a vector is defined.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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}
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* 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.
*
* 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.
*
* The symmetric gradient of a vector field $\mathbf v$ is defined as
* $\varepsilon(\mathbf v)=\frac 12 (\nabla \mathbf v + \nabla \mathbf
* v^T)$.
*
* @note There is no equivalent function such as
* FEValuesBase::get_function_symmetric_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.
*
* There is no equivalent function such as
* FEValuesBase::get_function_divergences 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.
*
* There is no equivalent function such as
* FEValuesBase::get_function_curls 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.
*
* 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. 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;
/**
* 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.
*
* This class allows to query the value and divergence of (components of)
* shape functions and solutions representing symmetric tensors. The
* divergence of a symmetric tensor $S_{ij}, 0\le i,j<\text{dim}$ is defined
* as $d_i = \sum_j \frac{\partial S_{ij}}{\partial x_j}, 0\le
* i<\text{dim}$, which due to the symmetry of the tensor is also $d_i =
* \sum_j \frac{\partial S_{ji}}{\partial x_j}$. In other words, it due to
* the symmetry of $S$ it does not matter whether we apply the nabla
* operator by row or by column to get the divergence.
*
* You get an object of this type if you apply a
* FEValuesExtractors::SymmetricTensor to an FEValues, FEFaceValues or
* FESubfaceValues object.
*
* @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>.
*
* See the general discussion of this class for a definition of the
* divergence.
*/
typedef dealii::Tensor<1, spacedim> divergence_type;
/**
* 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;
};
/**
* 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.
*
* @param shape_function Number of the shape function to be
* evaluated. Note that this number runs from zero to dofs_per_cell, even
* in the case of an FEFaceValues or FESubfaceValues object.
*
* @param q_point Number of the quadrature point at which function is to
* be evaluated
*/
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.
*
* See the general discussion of this class for a definition of the
* divergence.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* 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.
*
* There is no equivalent function such as
* FEValuesBase::get_function_divergences in the FEValues classes but the
* information can be obtained from FEValuesBase::get_function_gradients,
* of course.
*
* See the general discussion of this class for a definition of the
* divergence.
*/
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;
/**
* Store the data about shape functions.
*/
std::vector<ShapeFunctionData> shape_function_data;
};
template <int rank, int dim, int spacedim = dim>
class Tensor;
/**
* A class representing a view to a set of <code>dim*dim</code> components
* forming a second-order tensor from a vector-valued finite element. Views
* are discussed in the @ref vector_valued module.
*
* This class allows to query the value and divergence of (components of)
* shape functions and solutions representing tensors. The divergence of a
* tensor $T_{ij}, 0\le i,j<\text{dim}$ is defined as $d_i = \sum_j
* \frac{\partial T_{ji}}{\partial x_j}, 0\le i<\text{dim}$.
*
* You get an object of this type if you apply a FEValuesExtractors::Tensor
* to an FEValues, FEFaceValues or FESubfaceValues object.
*
* @ingroup feaccess vector_valued
*
* @author Denis Davydov, 2013
*/
template <int dim, int spacedim>
class Tensor<2,dim,spacedim>
{
public:
/**
* Data type for what you get when you apply an extractor of this kind to
* a vector-valued finite element.
*/
typedef dealii::Tensor<2, spacedim> value_type;
/**
* Data type for taking the divergence of a tensor: a vector.
*/
typedef dealii::Tensor<1, spacedim> divergence_type;
/**
* 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) 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;
};
/**
* Default constructor. Creates an invalid object.
*/
Tensor();
/**
* Constructor for an object that represents <code>(dim*dim)</code>
* components of a FEValuesBase object (or of one of the classes derived
* from FEValuesBase), representing the unique components comprising a
* second-order tensor valued variable.
*
* The second argument denotes the index of the first component of the
* selected symmetric second order tensor.
*/
Tensor(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.
*/
Tensor &operator=(const Tensor<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)</code> components (the unique
* components of a second-order tensor), the return type is a tensor of
* rank 2.
*
* @param shape_function Number of the shape function to be
* evaluated. Note that this number runs from zero to dofs_per_cell, even
* in the case of an FEFaceValues or FESubfaceValues object.
*
* @param q_point Number of the quadrature point at which function is to
* be evaluated
*/
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.
*
* See the general discussion of this class for a definition of the
* divergence.
*
* @note The meaning of the arguments is as documented for the value()
* function.
*/
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.
*
* 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.
*
* There is no equivalent function such as
* FEValuesBase::get_function_divergences in the FEValues classes but the
* information can be obtained from FEValuesBase::get_function_gradients,
* of course.
*
* See the general discussion of this class for a definition of the
* divergence.
*/
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;
/**
* 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;
std::vector<dealii::FEValuesViews::Tensor<2,dim,spacedim> >
second_order_tensors;
/**
* Constructor.
*/
Cache (const FEValuesBase<dim,spacedim> &fe_values);
};
}
}
//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.
*
* @ingroup feaccess
* @author Guido Kanschat
* @date 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< DerivativeForm<1,dim,spacedim> > jacobians;
/**
* Array of the derivatives of the Jacobian matrices at the quadrature
* points.
*/
std::vector<DerivativeForm<2,dim,spacedim> > jacobian_grads;
/**
* Array of the inverse Jacobian matrices at the quadrature points.
*/
std::vector<DerivativeForm<1,spacedim,dim> > 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;
/**
* When asked for the value (or gradient, or Hessian) of shape function i's
* c-th vector component, we need to look it up in the #shape_values,
* #shape_gradients and #shape_hessians arrays. The question is where in
* this array does the data for shape function i, component c reside. This is
* what this table answers.
*
* The format of the table is as
* follows:
* - It has dofs_per_cell times
* n_components entries.
* - The entry that corresponds to
* shape function i, component c
* is <code>i * n_components + c</code>.
* - The value stored at this
* position indicates the row
* in #shape_values and the
* other tables where the
* corresponding datum is stored
* for all the quadrature points.
*
* In the general, vector-valued context, the number of components is larger
* than one, but for a given shape function, not all vector components may be
* nonzero (e.g., if a shape function is primitive, then exactly one vector
* component is non-zero, while the others are all zero). For such zero
* components, #shape_values and friends do not have a row. Consequently, for
* vector components for which shape function i is zero, the entry in the
* current table is numbers::invalid_unsigned_int.
*
* On the other hand, the table is guaranteed to have at least one valid
* index for each shape function. In particular, for a primitive finite
* element, each shape function has exactly one nonzero component and so for
* each i, there is exactly one valid index within the range
* <code>[i*n_components, (i+1)*n_components)</code>.
*/
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.
*
* @ingroup feaccess
* @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 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.
*
* @param function_no Number of the shape function to be evaluated. Note
* that this number runs from zero to dofs_per_cell, even in the case of an
* FEFaceValues or FESubfaceValues object.
*
* @param point_no Number of the quadrature point at which function is to be
* evaluated
*/
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.
*
* @param function_no Number of the shape function to be evaluated
*
* @param point_no Number of the quadrature point at which function is to be
* evaluated
*
* @param component vector component to be evaluated
*/
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>function_no</tt>th shape function at the
* <tt>quadrature_point</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 of the Tensor returned by this function. 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 it will throw an exception of
* type ExcShapeFunctionNotPrimitive. In that case, use the
* shape_grad_component() function.
*
* The same holds for the arguments of this function as for the
* shape_value() function.
*/
const Tensor<1,spacedim> &
shape_grad (const unsigned int function_no,
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.
*
* The same holds for the arguments of this function as for the
* shape_value_component() function.
*/
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.
*
* The same holds for the arguments of this function as for the
* shape_value() 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 DEAL_II_DEPRECATED;
/**
* 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.
*
* The same holds for the arguments of this function as for the
* shape_value_component() function.
*/
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 DEAL_II_DEPRECATED;
//@}
/// @name Access to values of global finite element fields
//@{
/**
* Returns the values of a finite element function restricted to the current
* 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 active then values are interpolated to the
* current cell and point values are computed from that.
*
* This function may only be used if the finite element in use is a scalar
* one, i.e. has only one vector component. To get values of
* multi-component elements, there is another get_function_values() below,
* returning a vector of vectors of results.
*
* @param[in] fe_function A vector of values that describes (globally) the
* finite element function that this function should evaluate at the
* quadrature points of the current cell.
*
* @param[out] values The values of the function specified by fe_function at
* the quadrature points of the current cell. The object is assume to
* already have the correct size.
*
* @post <code>values[q]</code> will contain the value of the field
* described by fe_function at the $q$th quadrature point.
*
* @note 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. Alternatively, if the vector argument is of
* type IndexSet, then the function is represented as one that is either
* zero or one, depending on whether a DoF index is in the set or not.
*/
template <class InputVector, typename number>
void get_function_values (const InputVector &fe_function,
std::vector<number> &values) const;
/**
* This function does the same as the other get_function_values(), but
* applied to multi-component (vector-valued) elements. The meaning of the
* arguments is as explained there.
*
* @post <code>values[q]</code> is a vector of values of the field described
* by fe_function at the $q$th quadrature point. The size of the vector
* accessed by <code>values[q]</code> equals the number of components of the
* finite element, i.e. <code>values[q](c)</code> returns the value of the
* $c$th vector component at the $q$th quadrature point.
*/
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<types::global_dof_index> > &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<types::global_dof_index> > &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<types::global_dof_index> > &indices,
VectorSlice<std::vector<std::vector<double> > > values,
const bool quadrature_points_fastest) const;
//@}
/// @name Access to derivatives of global finite element fields
//@{
/**
* Compute the gradients of a finite element at the quadrature points of a
* cell. This function is the equivalent of the corresponding
* get_function_values() function (see there for more information) but
* evaluates the finite element field's gradient instead of its value.
*
* This function may only be used if the finite element in use is a scalar
* one, i.e. has only one vector component. There is a corresponding
* function of the same name for vector-valued finite elements.
*
* @param[in] fe_function A vector of values that describes (globally) the
* finite element function that this function should evaluate at the
* quadrature points of the current cell.
*
* @param[out] gradients The gradients of the function specified by
* fe_function at the quadrature points of the current cell. The gradients
* are computed in real space (as opposed to on the unit cell). The object
* is assume to already have the correct size.
*
* @post <code>gradients[q]</code> will contain the gradient of the field
* described by fe_function at the $q$th quadrature
* point. <code>gradients[q][d]</code> represents the derivative in
* coordinate direction $d$ at quadrature point $q$.
*
* @note 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. Alternatively, if the vector argument is of
* type IndexSet, then the function is represented as one that is either
* zero or one, depending on whether a DoF index is in the set or not.
*/
template <class InputVector>
void get_function_gradients (const InputVector &fe_function,
std::vector<Tensor<1,spacedim> > &gradients) const;
/**
* This function does the same as the other get_function_gradients(), but
* applied to multi-component (vector-valued) elements. The meaning of the
* arguments is as explained there.
*
* @post <code>gradients[q]</code> is a vector of gradients of the field
* described by fe_function at the $q$th quadrature point. The size of the
* vector accessed by <code>gradients[q]</code> equals the number of
* components of the finite element, i.e. <code>gradients[q][c]</code>
* returns the gradient of the $c$th vector component at the $q$th
* quadrature point. Consequently, <code>gradients[q][c][d]</code> is the
* derivative in coordinate direction $d$ of the $c$th vector component of
* the vector field at quadrature point $q$ of the current cell.
*/
template <class InputVector>
void get_function_gradients (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<types::global_dof_index> > &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<types::global_dof_index> > &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,
std::vector<Tensor<1,spacedim> > &gradients) const DEAL_II_DEPRECATED;
/**
* @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 DEAL_II_DEPRECATED;
/**
* @deprecated Use get_function_gradients() instead.
*/
template <class InputVector>
void get_function_grads (const InputVector &fe_function,
const VectorSlice<const std::vector<types::global_dof_index> > &indices,
std::vector<Tensor<1,spacedim> > &gradients) const DEAL_II_DEPRECATED;
/**
* @deprecated Use get_function_gradients() instead.
*/
template <class InputVector>
void get_function_grads (const InputVector &fe_function,
const VectorSlice<const std::vector<types::global_dof_index> > &indices,
std::vector<std::vector<Tensor<1,spacedim> > > &gradients,
bool quadrature_points_fastest = false) const DEAL_II_DEPRECATED;
//@}
/// @name Access to second derivatives (Hessian matrices and Laplacians) of global finite element fields
//@{
/**
* Compute the tensor of second derivatives of a finite element at the
* quadrature points of a cell. This function is the equivalent of the
* corresponding get_function_values() function (see there for more
* information) but evaluates the finite element field's second derivatives
* instead of its value.
*
* This function may only be used if the finite element in use is a scalar
* one, i.e. has only one vector component. There is a corresponding
* function of the same name for vector-valued finite elements.
*
* @param[in] fe_function A vector of values that describes (globally) the
* finite element function that this function should evaluate at the
* quadrature points of the current cell.
*
* @param[out] hessians The Hessians of the function specified by
* fe_function at the quadrature points of the current cell. The Hessians
* are computed in real space (as opposed to on the unit cell). The object
* is assume to already have the correct size.
*
* @post <code>hessians[q]</code> will contain the Hessian of the field
* described by fe_function at the $q$th quadrature
* point. <code>gradients[q][i][j]</code> represents the $(i,j)$th component
* of the matrix of second derivatives at quadrature point $q$.
*
* @note 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. Alternatively, if the vector argument is of
* type IndexSet, then the function is represented as one that is either
* zero or one, depending on whether a DoF index is in the set or not.
*/
template <class InputVector>
void
get_function_hessians (const InputVector &fe_function,
std::vector<Tensor<2,spacedim> > &hessians) const;
/**
* This function does the same as the other get_function_hessians(), but
* applied to multi-component (vector-valued) elements. The meaning of the
* arguments is as explained there.
*
* @post <code>hessians[q]</code> is a vector of Hessians of the field
* described by fe_function at the $q$th quadrature point. The size of the
* vector accessed by <code>hessians[q]</code> equals the number of
* components of the finite element, i.e. <code>hessians[q][c]</code>
* returns the Hessian of the $c$th vector component at the $q$th quadrature
* point. Consequently, <code>values[q][c][i][j]</code> is the $(i,j)$th
* component of the matrix of second derivatives of the $c$th vector
* component of the vector field at quadrature point $q$ of the current
* 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<types::global_dof_index> > &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<types::global_dof_index> > &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 DEAL_II_DEPRECATED;
/**
* @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 DEAL_II_DEPRECATED;
/**
* Compute the (scalar) Laplacian (i.e. the trace of the tensor of second
* derivatives) of a finite element at the quadrature points of a cell. This
* function is the equivalent of the corresponding get_function_values()
* function (see there for more information) but evaluates the finite
* element field's second derivatives instead of its value.
*
* This function may only be used if the finite element in use is a scalar
* one, i.e. has only one vector component. There is a corresponding
* function of the same name for vector-valued finite elements.
*
* @param[in] fe_function A vector of values that describes (globally) the
* finite element function that this function should evaluate at the
* quadrature points of the current cell.
*
* @param[out] laplacians The Laplacians of the function specified by
* fe_function at the quadrature points of the current cell. The Laplacians
* are computed in real space (as opposed to on the unit cell). The object
* is assume to already have the correct size.
*
* @post <code>laplacians[q]</code> will contain the Laplacian of the field
* described by fe_function at the $q$th quadrature
* point. <code>gradients[q][i][j]</code> represents the $(i,j)$th component
* of the matrix of second derivatives at quadrature point $q$.
*
* @post For each component of the output vector, there holds
* <code>laplacians[q]=trace(hessians[q])</code>, where <tt>hessians</tt>
* would be the output of the get_function_hessians() function.
*
* @note 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. Alternatively, if the vector argument is of
* type IndexSet, then the function is represented as one that is either
* zero or one, depending on whether a DoF index is in the set or not.
*/
template <class InputVector, typename number>
void
get_function_laplacians (const InputVector &fe_function,
std::vector<number> &laplacians) const;
/**
* This function does the same as the other get_function_laplacians(), but
* applied to multi-component (vector-valued) elements. The meaning of the
* arguments is as explained there.
*
* @post <code>laplacians[q]</code> is a vector of Laplacians of the field
* described by fe_function at the $q$th quadrature point. The size of the
* vector accessed by <code>laplacians[q]</code> equals the number of
* components of the finite element, i.e. <code>laplacians[q][c]</code>
* returns the Laplacian of the $c$th vector component at the $q$th
* quadrature point.
*
* @post For each component of the output vector, there holds
* <code>laplacians[q][c]=trace(hessians[q][c])</code>, where
* <tt>hessians</tt> would be the output of the get_function_hessians()
* function.
*/
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<types::global_dof_index> > &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<types::global_dof_index> > &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<types::global_dof_index> > &indices,
std::vector<std::vector<number> > &laplacians,
bool quadrature_points_fastest = false) const;
//@}
/// @name Geometry of the cell
//@{
/**
* 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 in real space.
*/
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 DerivativeForm<1,dim,spacedim> &jacobian (const unsigned int quadrature_point) const;
/**
* Pointer to the array holding the values returned by jacobian().
*/
const std::vector<DerivativeForm<1,dim,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 DerivativeForm<2,dim,spacedim> &jacobian_grad (const unsigned int quadrature_point) const;
/**
* Pointer to the array holding the values returned by jacobian_grads().
*/
const std::vector<DerivativeForm<2,dim,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 DerivativeForm<1,spacedim,dim> &inverse_jacobian (const unsigned int quadrature_point) const;
/**
* Pointer to the array holding the values returned by inverse_jacobian().
*/
const std::vector<DerivativeForm<1,spacedim,dim> > &get_inverse_jacobians () 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;
/**
* Transform a set of vectors, one for each quadrature point. The
* <tt>mapping</tt> can be any of the ones defined in MappingType.
*/
void transform (std::vector<Tensor<1,spacedim> > &transformed,
const std::vector<Tensor<1,dim> > &original,
MappingType mapping) 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 DEAL_II_DEPRECATED;
/**
* @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 DEAL_II_DEPRECATED;
//@}
/// @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;
/**
* Create a view of the current FEValues object that represents a set of
* <code>(dim*dim)</code> scalar components (i.e. a 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::Tensor<2,dim,spacedim> &
operator[] (const FEValuesExtractors::Tensor<2> &tensor) const;
//@}
/// @name Access to the raw data
//@{
/**
* 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;
/**
* 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.
*/
std::size_t 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
*/
DeclException1 (ExcAccessToUninitializedField,
char *,
<< ("You are requesting information from an FEValues/FEFaceValues/FESubfaceValues "
"object for which this kind of information has not been computed. What "
"information these objects compute is determined by the update_* flags you "
"pass to the constructor. Here, the operation you are attempting requires "
"the <")
<< arg1
<< "> flag to be set, but it was apparently not specified upon construction.");
/**
* @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;
/**
* A signal connection we use to ensure we get informed whenever the
* triangulation changes. We need to know about that because it invalidates
* all cell iterators and, as part of that, the 'present_cell' iterator we
* keep around between subsequent calls to reinit() in order to compute the
* cell similarity.
*/
boost::signals2::connection tria_listener;
/**
* A function that is connected to the triangulation in order to reset the
* stored 'present_cell' iterator to an invalid one whenever the
* triangulation is changed and the iterator consequently becomes invalid.
*/
void invalidate_present_cell ();
/**
* This function is called by the various reinit() functions in derived
* classes. Given the cell indicated by the argument, test whether we have
* to throw away the previously stored present_cell argument because it
* would require us to compare cells from different triangulations. In
* checking all this, also make sure that we have tria_listener connected to
* the triangulation to which we will set present_cell right after calling
* this function.
*/
void
maybe_invalidate_previous_present_cell (const typename Triangulation<dim,spacedim>::cell_iterator &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.
*/
dealii::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;
template <int, int, int> friend class FEValuesViews::Tensor;
};
/**
* 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.
*
* @ingroup feaccess
* @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.
*/
template <class DH, bool level_dof_access>
void reinit (const TriaIterator<DoFCellAccessor<DH,level_dof_access> > 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.
*/
std::size_t 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.
*
* See FEValuesBase
*
* @ingroup feaccess
* @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. See @ref GlossBoundaryForm .
*/
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.
*/
std::size_t 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.
*
* @ingroup feaccess
* @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.
*/
template <class DH, bool level_dof_access>
void reinit (const TriaIterator<DoFCellAccessor<DH,level_dof_access> > 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.
*
* @ingroup feaccess
* @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.
*/
template <class DH, bool level_dof_access>
void reinit (const TriaIterator<DoFCellAccessor<DH,level_dof_access> > 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 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("update_values"));
// 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("update_gradients"));
// 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("update_hessians"));
// 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("update_values"));
// 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("update_gradients"));
// 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("update_gradients"));
// 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("update_gradients"));
// 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;
// the single
// nonzero component
// can only be zero
// or one in 2d
if (shape_function_data[shape_function].single_nonzero_component_index == 0)
return_value[0] = -1.0 * fe_values.shape_gradients[snc][q_point][1];
else
return_value[0] = fe_values.shape_gradients[snc][q_point][0];
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;
}
}
}
// should not end up here
Assert (false, ExcInternalError());
return curl_type();
}
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("update_hessians"));
// 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 dealii::Tensor<1,1> &t)
{
Assert (n < 1, ExcIndexRange (n, 0, 1));
(void)n; // removes -Wunused-parameter warning in optimized mode
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 dealii::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 dealii::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("update_gradients"));
// 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);
}
}
template <int dim, int spacedim>
inline
typename SymmetricTensor<2, dim, spacedim>::value_type
SymmetricTensor<2, 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("update_values"));
// similar to the vector case where we
// have more then one index and we need
// to convert between unrolled and
// component indexing for tensors
const int snc
= shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
{
// shape function is zero for the
// selected components
return value_type();
}
else if (snc != -1)
{
value_type return_value;
const unsigned int comp =
shape_function_data[shape_function].single_nonzero_component_index;
return_value[value_type::unrolled_to_component_indices(comp)]
= fe_values.shape_values(snc,q_point);
return return_value;
}
else
{
value_type return_value;
for (unsigned int d = 0; d < value_type::n_independent_components; ++d)
if (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
return_value[value_type::unrolled_to_component_indices(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 SymmetricTensor<2, dim, spacedim>::divergence_type
SymmetricTensor<2, dim, spacedim>::divergence(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("update_gradients"));
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
{
// shape function is zero for the
// selected components
return divergence_type();
}
else if (snc != -1)
{
// we have a single non-zero component
// when the symmetric tensor is
// represented in unrolled form.
// this implies we potentially have
// two non-zero components when
// represented in component form! we
// will only have one non-zero entry
// if the non-zero component lies on
// the diagonal of the tensor.
//
// the divergence of a second-order tensor
// is a first order tensor.
//
// assume the second-order tensor is
// A with components A_{ij}. then
// A_{ij} = A_{ji} and there is only
// one (if diagonal) or two non-zero
// entries in the tensorial
// representation. define the
// divergence as:
// b_i := \dfrac{\partial phi_{ij}}{\partial x_j}.
// (which is incidentally also
// b_j := \dfrac{\partial phi_{ij}}{\partial x_i}).
// In both cases, a sum is implied.
//
// Now, we know the nonzero component
// in unrolled form: it is indicated
// by 'snc'. we can figure out which
// tensor components belong to this:
const unsigned int comp =
shape_function_data[shape_function].single_nonzero_component_index;
const unsigned int ii = value_type::unrolled_to_component_indices(comp)[0];
const unsigned int jj = value_type::unrolled_to_component_indices(comp)[1];
// given the form of the divergence
// above, if ii=jj there is only a
// single nonzero component of the
// full tensor and the gradient
// equals
// b_ii := \dfrac{\partial phi_{ii,ii}}{\partial x_ii}.
// all other entries of 'b' are zero
//
// on the other hand, if ii!=jj, then
// there are two nonzero entries in
// the full tensor and
// b_ii := \dfrac{\partial phi_{ii,jj}}{\partial x_ii}.
// b_jj := \dfrac{\partial phi_{ii,jj}}{\partial x_jj}.
// again, all other entries of 'b' are
// zero
const dealii::Tensor<1, spacedim> phi_grad = fe_values.shape_gradients[snc][q_point];
divergence_type return_value;
return_value[ii] = phi_grad[jj];
if (ii != jj)
return_value[jj] = phi_grad[ii];
return return_value;
}
else
{
Assert (false, ExcNotImplemented());
divergence_type return_value;
return return_value;
}
}
template <int dim, int spacedim>
inline
typename Tensor<2, dim, spacedim>::value_type
Tensor<2, 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("update_values"));
// similar to the vector case where we
// have more then one index and we need
// to convert between unrolled and
// component indexing for tensors
const int snc
= shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
{
// shape function is zero for the
// selected components
return value_type();
}
else if (snc != -1)
{
value_type return_value;
const unsigned int comp =
shape_function_data[shape_function].single_nonzero_component_index;
const TableIndices<2> indices = dealii::Tensor<2,spacedim>::unrolled_to_component_indices(comp);
return_value[indices] = fe_values.shape_values(snc,q_point);
return return_value;
}
else
{
value_type return_value;
for (unsigned int d = 0; d < dim*dim; ++d)
if (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
{
const TableIndices<2> indices = dealii::Tensor<2,spacedim>::unrolled_to_component_indices(d);
return_value[indices]
= fe_values.shape_values(shape_function_data[shape_function].row_index[d],q_point);
}
return return_value;
}
}
template <int dim, int spacedim>
inline
typename Tensor<2, dim, spacedim>::divergence_type
Tensor<2, dim, spacedim>::divergence(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("update_gradients"));
const int snc = shape_function_data[shape_function].single_nonzero_component;
if (snc == -2)
{
// shape function is zero for the
// selected components
return divergence_type();
}
else if (snc != -1)
{
// we have a single non-zero component
// when the tensor is
// represented in unrolled form.
//
// the divergence of a second-order tensor
// is a first order tensor.
//
// assume the second-order tensor is
// A with components A_{ij}.
// divergence as:
// b_j := \dfrac{\partial phi_{ij}}{\partial x_i}.
//
// Now, we know the nonzero component
// in unrolled form: it is indicated
// by 'snc'. we can figure out which
// tensor components belong to this:
const unsigned int comp =
shape_function_data[shape_function].single_nonzero_component_index;
const TableIndices<2> indices = dealii::Tensor<2,spacedim>::unrolled_to_component_indices(comp);
const unsigned int ii = indices[0];
const unsigned int jj = indices[1];
const dealii::Tensor<1, spacedim> phi_grad = fe_values.shape_gradients[snc][q_point];
divergence_type return_value;
return_value[jj] = phi_grad[ii];
return return_value;
}
else
{
Assert (false, ExcNotImplemented());
divergence_type return_value;
return 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 FEValuesViews::Tensor<2,dim,spacedim> &
FEValuesBase<dim,spacedim>::
operator[] (const FEValuesExtractors::Tensor<2> &tensor) const
{
Assert (tensor.first_tensor_component <
fe_values_views_cache.second_order_tensors.size(),
ExcIndexRange (tensor.first_tensor_component,
0, fe_values_views_cache.second_order_tensors.size()));
return fe_values_views_cache.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("update_values"));
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 we can call
// system_to_component_index
const unsigned int
row = this->shape_function_to_row_table[i * fe->n_components() + fe->system_to_component_index(i).first];
return this->shape_values(row, 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("update_values"));
Assert (component < fe->n_components(),
ExcIndexRange(component, 0, fe->n_components()));
// check whether the shape function
// is non-zero at all within
// this component:
if (fe->get_nonzero_components(i)[component] == false)
return 0;
// look up the right row in the
// table and take the data from
// there
const unsigned int
row = this->shape_function_to_row_table[i * fe->n_components() + component];
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("update_gradients"));
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 we can call
// system_to_component_index
const unsigned int
row = this->shape_function_to_row_table[i * fe->n_components() + fe->system_to_component_index(i).first];
return this->shape_gradients[row][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("update_gradients"));
Assert (component < fe->n_components(),
ExcIndexRange(component, 0, fe->n_components()));
// 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>();
// look up the right row in the
// table and take the data from
// there
const unsigned int
row = this->shape_function_to_row_table[i * fe->n_components() + component];
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("update_hessians"));
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 we can call
// system_to_component_index
const unsigned int
row = this->shape_function_to_row_table[i * fe->n_components() + fe->system_to_component_index(i).first];
return this->shape_hessians[row][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("update_hessians"));
Assert (component < fe->n_components(),
ExcIndexRange(component, 0, fe->n_components()));
// 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>();
// look up the right row in the
// table and take the data from
// there
const unsigned int
row = this->shape_function_to_row_table[i * fe->n_components() + component];
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("update_quadrature_points"));
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("update_JxW_values"));
return this->JxW_values;
}
template <int dim, int spacedim>
inline
const std::vector<DerivativeForm<1,dim,spacedim> > &
FEValuesBase<dim,spacedim>::get_jacobians () const
{
Assert (this->update_flags & update_jacobians,
ExcAccessToUninitializedField("update_jacobians"));
return this->jacobians;
}
template <int dim, int spacedim>
inline
const std::vector<DerivativeForm<2,dim,spacedim> > &
FEValuesBase<dim,spacedim>::get_jacobian_grads () const
{
Assert (this->update_flags & update_jacobian_grads,
ExcAccessToUninitializedField("update_jacobians_grads"));
return this->jacobian_grads;
}
template <int dim, int spacedim>
inline
const std::vector<DerivativeForm<1,spacedim,dim> > &
FEValuesBase<dim,spacedim>::get_inverse_jacobians () const
{
Assert (this->update_flags & update_inverse_jacobians,
ExcAccessToUninitializedField("update_inverse_jacobians"));
return this->inverse_jacobians;
}
template <int dim, int spacedim>
inline
const Point<spacedim> &
FEValuesBase<dim,spacedim>::quadrature_point (const unsigned int i) const
{
Assert (this->update_flags & update_quadrature_points,
ExcAccessToUninitializedField("update_quadrature_points"));
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("update_JxW_values"));
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 DerivativeForm<1,dim,spacedim> &
FEValuesBase<dim,spacedim>::jacobian (const unsigned int i) const
{
Assert (this->update_flags & update_jacobians,
ExcAccessToUninitializedField("update_jacobians"));
Assert (i<this->jacobians.size(), ExcIndexRange(i, 0, this->jacobians.size()));
return this->jacobians[i];
}
template <int dim, int spacedim>
inline
const DerivativeForm<2,dim,spacedim> &
FEValuesBase<dim,spacedim>::jacobian_grad (const unsigned int i) const
{
Assert (this->update_flags & update_jacobian_grads,
ExcAccessToUninitializedField("update_jacobians_grads"));
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 DerivativeForm<1,spacedim,dim> &
FEValuesBase<dim,spacedim>::inverse_jacobian (const unsigned int i) const
{
Assert (this->update_flags & update_inverse_jacobians,
ExcAccessToUninitializedField("update_inverse_jacobians"));
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<types::global_dof_index> > &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<types::global_dof_index> > &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("update_normal_vectors"));
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("update_boundary_forms"));
return this->boundary_forms[i];
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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