FEValuesViews::Vector< dim > Class Template Reference
[Finite element access/FEValues classesHandling vector valued problems]

List of all members.

Public Types

typedef Tensor< 1, dim > value_type
typedef Tensor< 2, dim > gradient_type
typedef SymmetricTensor< 2, dim > symmetric_gradient_type
typedef double divergence_type
typedef Tensor< 3, dim > hessian_type

Public Member Functions

 Vector (const FEValuesBase< dim > &fe_values_base, const unsigned int first_vector_component)
value_type value (const unsigned int shape_function, const unsigned int q_point) const
gradient_type gradient (const unsigned int shape_function, const unsigned int q_point) const
symmetric_gradient_type symmetric_gradient (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
hessian_type hessian (const unsigned int shape_function, const unsigned int q_point) const

Private Attributes

const FEValuesBase< dim > & fe_values
const unsigned int first_vector_component


Detailed Description

template<int dim>
class FEValuesViews::Vector< dim >

A class representing a view to a set of dim components forming a vector part of a vector-valued finite element. Views are discussed in the Handling vector valued problems module.

Member Typedef Documentation

template<int dim>
typedef Tensor<1,dim> FEValuesViews::Vector< dim >::value_type

A typedef for the data type of values of the view this class represents. Since we deal with a set of dim components, the value type is a Tensor<1,dim>.

template<int dim>
typedef Tensor<2,dim> FEValuesViews::Vector< dim >::gradient_type

A typedef for the type of gradients of the view this class represents. Here, for a set of dim components of the finite element, the gradient is a Tensor<2,dim>.

template<int dim>
typedef SymmetricTensor<2,dim> FEValuesViews::Vector< dim >::symmetric_gradient_type

A typedef for the type of symmetrized gradients of the view this class represents. Here, for a set of dim components of the finite element, the symmetrized gradient is a SymmetricTensor<2,dim>.

template<int dim>
typedef double FEValuesViews::Vector< dim >::divergence_type

A typedef for the type of the divergence of the view this class represents. Here, for a set of dim components of the finite element, the divergence of course is a scalar.

template<int dim>
typedef Tensor<3,dim> FEValuesViews::Vector< dim >::hessian_type

A typedef for the type of second derivatives of the view this class represents. Here, for a set of dim components of the finite element, the Hessian is a Tensor<3,dim>.


Constructor & Destructor Documentation

template<int dim>
FEValuesViews::Vector< dim >::Vector ( const FEValuesBase< dim > &  fe_values_base,
const unsigned int  first_vector_component 
)

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.


Member Function Documentation

template<int dim>
value_type FEValuesViews::Vector< dim >::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 components, the return type is a tensor of rank 1 with dim components.

template<int dim>
gradient_type FEValuesViews::Vector< dim >::gradient ( 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.

template<int dim>
symmetric_gradient_type FEValuesViews::Vector< dim >::symmetric_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 dim components selected from the FEValuesBase object, and $x_q$ is the location of the $q$-th quadrature point.

template<int dim>
divergence_type FEValuesViews::Vector< dim >::divergence ( 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.

template<int dim>
hessian_type FEValuesViews::Vector< dim >::hessian ( 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.


Member Data Documentation

template<int dim>
const FEValuesBase<dim>& FEValuesViews::Vector< dim >::fe_values [private]

A reference to the FEValuesBase object we operator on.

template<int dim>
const unsigned int FEValuesViews::Vector< dim >::first_vector_component [private]

The first component of the vector this view represents of the FEValuesBase object.


The documentation for this class was generated from the following file:

deal.II documentation generated on Fri Nov 21 07:13:44 2008 by doxygen 1.5.6