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Reference documentation for deal.II version 9.6.0
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#include <deal.II/fe/fe_values_views.h>
Classes | |
struct | ShapeFunctionData |
Public Types | |
using | value_type = ::SymmetricTensor<2, spacedim> |
using | divergence_type = ::Tensor<1, spacedim> |
template<typename Number > | |
using | solution_value_type = typename ProductType<Number, value_type>::type |
template<typename Number > | |
using | solution_divergence_type |
Public Member Functions | |
SymmetricTensor () | |
SymmetricTensor (const FEValuesBase< dim, spacedim > &fe_values_base, const unsigned int first_tensor_component) | |
SymmetricTensor (const SymmetricTensor< 2, dim, spacedim > &)=delete | |
SymmetricTensor (SymmetricTensor< 2, dim, spacedim > &&)=default | |
SymmetricTensor & | operator= (const SymmetricTensor< 2, dim, spacedim > &)=delete |
SymmetricTensor & | operator= (SymmetricTensor< 2, dim, spacedim > &&) noexcept=default |
value_type | value (const unsigned int shape_function, const unsigned int q_point) const |
divergence_type | divergence (const unsigned int shape_function, const unsigned int q_point) const |
template<typename Number > | |
void | get_function_values (const ReadVector< Number > &fe_function, std::vector< solution_value_type< Number > > &values) const |
template<class InputVector > | |
void | get_function_values_from_local_dof_values (const InputVector &dof_values, std::vector< solution_value_type< typename InputVector::value_type > > &values) const |
template<typename Number > | |
void | get_function_divergences (const ReadVector< Number > &fe_function, std::vector< solution_divergence_type< Number > > &divergences) const |
template<class InputVector > | |
void | get_function_divergences_from_local_dof_values (const InputVector &dof_values, std::vector< solution_divergence_type< typename InputVector::value_type > > &divergences) const |
Private Attributes | |
SmartPointer< const FEValuesBase< dim, spacedim > > | fe_values |
unsigned int | first_tensor_component |
std::vector< ShapeFunctionData > | shape_function_data |
A class representing a view to a set of (dim*dim + dim)/2
components forming a symmetric second-order tensor from a vector-valued finite element. Views are discussed in the Handling vector valued problems topic.
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.
Definition at line 1315 of file fe_values_views.h.
using FEValuesViews::SymmetricTensor< 2, dim, spacedim >::value_type = ::SymmetricTensor<2, spacedim> |
An alias for the data type of values of the view this class represents. Since we deal with a set of (dim*dim + dim)/2
components (i.e. the unique components of a symmetric second-order tensor), the value type is a SymmetricTensor<2,spacedim>.
Definition at line 1324 of file fe_values_views.h.
using FEValuesViews::SymmetricTensor< 2, dim, spacedim >::divergence_type = ::Tensor<1, spacedim> |
An alias for the type of the divergence of the view this class represents. Here, for a set of (dim*dim + dim)/2
unique components of the finite element representing a symmetric second-order tensor, the divergence of course is a * Tensor<1,dim>
.
See the general discussion of this class for a definition of the divergence.
Definition at line 1335 of file fe_values_views.h.
using FEValuesViews::SymmetricTensor< 2, dim, spacedim >::solution_value_type = typename ProductType<Number, value_type>::type |
An alias for the data type of the product of a Number
and the values of the view this class provides. This is the data type of vector components of a finite element field whose degrees of freedom are described by a vector with elements of type Number
.
Definition at line 1344 of file fe_values_views.h.
using FEValuesViews::SymmetricTensor< 2, dim, spacedim >::solution_divergence_type |
An alias for the data type of the product of a Number
and the divergences of the view this class provides. This is the data type of vector components of a finite element field whose degrees of freedom are described by a vector with elements of type Number
.
Definition at line 1353 of file fe_values_views.h.
FEValuesViews::SymmetricTensor< 2, dim, spacedim >::SymmetricTensor | ( | ) |
Default constructor. Creates an invalid object.
Definition at line 274 of file fe_values_views.cc.
FEValuesViews::SymmetricTensor< 2, dim, spacedim >::SymmetricTensor | ( | const FEValuesBase< dim, spacedim > & | fe_values_base, |
const unsigned int | first_tensor_component ) |
Constructor for an object that represents (dim*dim + dim)/2
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.
Definition at line 192 of file fe_values_views.cc.
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delete |
Copy constructor. This is not a lightweight object so we don't allow copying and generate a compile-time error if this function is called.
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default |
Move constructor.
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delete |
Copy operator. This is not a lightweight object so we don't allow copying and generate a compile-time error if this function is called.
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defaultnoexcept |
Move assignment operator.
value_type FEValuesViews::SymmetricTensor< 2, dim, spacedim >::value | ( | const unsigned int | shape_function, |
const unsigned int | q_point ) const |
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 (dim*dim + dim)/2
components (the unique components of a symmetric second-order tensor), the return type is a symmetric tensor of rank 2.
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. |
q_point | Number of the quadrature point at which function is to be evaluated. |
update_values
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. divergence_type FEValuesViews::SymmetricTensor< 2, dim, spacedim >::divergence | ( | 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.
update_gradients
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. void FEValuesViews::SymmetricTensor< 2, dim, spacedim >::get_function_values | ( | const ReadVector< Number > & | fe_function, |
std::vector< solution_value_type< Number > > & | values ) const |
Return the values of the selected vector components of the finite element function characterized by fe_function
at the quadrature points of the cell, face or subface selected the last time the reinit
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.
The data type stored by the output vector must be what you get when you multiply the values of shape functions (i.e., value_type
) times the type used to store the values of the unknowns \(U_j\) of your finite element vector \(U\) (represented by the fe_function
argument).
update_values
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1049 of file fe_values_views.cc.
void FEValuesViews::SymmetricTensor< 2, dim, spacedim >::get_function_values_from_local_dof_values | ( | const InputVector & | dof_values, |
std::vector< solution_value_type< typename InputVector::value_type > > & | values ) const |
Same as above, but using a vector of local degree-of-freedom values. In other words, instead of extracting the nodal values of the degrees of freedom located on the current cell from a global vector associated with a DoFHandler object (as the function above does), this function instead takes these local nodal values through its first argument. A typical way to obtain such a vector is by calling code such as
(See DoFCellAccessor::get_dof_values() for more information on this function.) The point of the current function is then that one could modify these local values first, for example by applying a limiter or by ensuring that all nodal values are positive, before evaluating the finite element field that corresponds to these local values on the current cell. Another application is where one wants to postprocess the solution on a cell into a different finite element space on every cell, without actually creating a corresponding DoFHandler – in that case, all one would compute is a local representation of that postprocessed function, characterized by its nodal values; this function then allows the evaluation of that representation at quadrature points.
[in] | dof_values | A vector of local nodal values. This vector must have a length equal to number of DoFs on the current cell, and must be ordered in the same order as degrees of freedom are numbered on the reference cell. |
[out] | values | A vector of values of the given finite element field, at the quadrature points on the current object. |
InputVector | The InputVector type must allow creation of an ArrayView object from it; this is satisfied by the std::vector class, among others. |
Definition at line 1075 of file fe_values_views.cc.
void FEValuesViews::SymmetricTensor< 2, dim, spacedim >::get_function_divergences | ( | const ReadVector< Number > & | fe_function, |
std::vector< solution_divergence_type< Number > > & | divergences ) const |
Return the divergence of the selected vector components of the finite element function characterized by fe_function
at the quadrature points of the cell, face or subface selected the last time the reinit
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.
The data type stored by the output vector must be what you get when you multiply the divergences of shape functions (i.e., divergence_type
) times the type used to store the values of the unknowns \(U_j\) of your finite element vector \(U\) (represented by the fe_function
argument).
update_gradients
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1099 of file fe_values_views.cc.
void FEValuesViews::SymmetricTensor< 2, dim, spacedim >::get_function_divergences_from_local_dof_values | ( | const InputVector & | dof_values, |
std::vector< solution_divergence_type< typename InputVector::value_type > > & | divergences ) const |
This function relates to get_function_divergences() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information.
Definition at line 1128 of file fe_values_views.cc.
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private |
A pointer to the FEValuesBase object we operate on.
Definition at line 1587 of file fe_values_views.h.
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private |
The first component of the vector this view represents of the FEValuesBase object.
Definition at line 1593 of file fe_values_views.h.
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private |
Store the data about shape functions.
Definition at line 1598 of file fe_values_views.h.