FEValuesData< dim, spacedim > Class Template Reference
[Finite element access/FEValues classes]

Inheritance diagram for FEValuesData< dim, spacedim >:
Inheritance graph
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List of all members.

Public Types

typedef Table< 2, doubleShapeVector
typedef std::vector
< std::vector< Tensor
< 1, spacedim > > > 
GradientVector
typedef std::vector
< std::vector< Tensor
< 2, spacedim > > > 
HessianVector

Public Member Functions

void initialize (const unsigned int n_quadrature_points, const FiniteElement< dim, spacedim > &fe, const UpdateFlags flags)

Public Attributes

ShapeVector shape_values
GradientVector shape_gradients
HessianVector shape_hessians
std::vector< doubleJxW_values
std::vector< Tensor
< 2, spacedim > > 
jacobians
std::vector< Tensor
< 3, spacedim > > 
jacobian_grads
std::vector< Tensor
< 2, spacedim > > 
inverse_jacobians
std::vector< Point< spacedim > > quadrature_points
std::vector< Point< spacedim > > normal_vectors
std::vector< Point< spacedim > > cell_normal_vectors
std::vector< Tensor
< 1, spacedim > > 
boundary_forms
std::vector< Point< spacedim > > support_points
HessianVector support_jacobians
HessianVector support_inverse_jacobians
std::vector< unsigned intshape_function_to_row_table
UpdateFlags update_flags

Detailed Description

template<int dim, int spacedim = dim>
class FEValuesData< dim, spacedim >

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 The interplay of UpdateFlags, Mapping and FiniteElement in FEValues.

Author:
Guido Kanschat, 2000

Member Typedef Documentation

template<int dim, int spacedim = dim>
typedef Table<2,double> FEValuesData< dim, spacedim >::ShapeVector

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.

template<int dim, int spacedim = dim>
typedef std::vector<std::vector<Tensor<1,spacedim> > > FEValuesData< dim, spacedim >::GradientVector

Storage type for gradients. The layout of data is the same as for the ShapeVector data type.

template<int dim, int spacedim = dim>
typedef std::vector<std::vector<Tensor<2,spacedim> > > FEValuesData< dim, spacedim >::HessianVector

Likewise for second order derivatives.


Member Function Documentation

template<int dim, int spacedim = dim>
void FEValuesData< dim, spacedim >::initialize ( const unsigned int  n_quadrature_points,
const FiniteElement< dim, spacedim > &  fe,
const UpdateFlags  flags 
)

Initialize all vectors to correct size.


Member Data Documentation

template<int dim, int spacedim = dim>
ShapeVector FEValuesData< dim, spacedim >::shape_values

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.

template<int dim, int spacedim = dim>
GradientVector FEValuesData< dim, spacedim >::shape_gradients

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.

template<int dim, int spacedim = dim>
HessianVector FEValuesData< dim, spacedim >::shape_hessians

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.

template<int dim, int spacedim = dim>
std::vector<double> FEValuesData< dim, spacedim >::JxW_values

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.

template<int dim, int spacedim = dim>
std::vector<Tensor<2,spacedim> > FEValuesData< dim, spacedim >::jacobians

Array of the Jacobian matrices at the quadrature points.

template<int dim, int spacedim = dim>
std::vector<Tensor<3,spacedim> > FEValuesData< dim, spacedim >::jacobian_grads

Array of the derivatives of the Jacobian matrices at the quadrature points.

template<int dim, int spacedim = dim>
std::vector<Tensor<2,spacedim> > FEValuesData< dim, spacedim >::inverse_jacobians

Array of the inverse Jacobian matrices at the quadrature points.

template<int dim, int spacedim = dim>
std::vector<Point<spacedim> > FEValuesData< dim, spacedim >::quadrature_points

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.

template<int dim, int spacedim = dim>
std::vector<Point<spacedim> > FEValuesData< dim, spacedim >::normal_vectors

List of outward normal vectors at the quadrature points. This field is filled in by the finite element class.

template<int dim, int spacedim = dim>
std::vector<Point<spacedim> > FEValuesData< dim, spacedim >::cell_normal_vectors

List of outward vectors normal to the cell surface (line) at the quadrature points for the codimension 1 case, when spacedim=3 (=2).

template<int dim, int spacedim = dim>
std::vector<Tensor<1,spacedim> > FEValuesData< dim, spacedim >::boundary_forms

List of boundary forms at the quadrature points. This field is filled in by the finite element class.

template<int dim, int spacedim = dim>
std::vector<Point<spacedim> > FEValuesData< dim, spacedim >::support_points

Array of the mapped support points, filled by Mapping.

template<int dim, int spacedim = dim>
HessianVector FEValuesData< dim, spacedim >::support_jacobians

Array of the Jacobian of the mapping in the support points, filled by Mapping.

template<int dim, int spacedim = dim>
HessianVector FEValuesData< dim, spacedim >::support_inverse_jacobians

Array of the inverse Jacobian of the mapping in the support points, filled by Mapping.

template<int dim, int spacedim = dim>
std::vector<unsigned int> FEValuesData< dim, spacedim >::shape_function_to_row_table

Indicate the first row which a given shape function occupies in the shape_values, shape_gradients and shape_hessians arrays. If all shape functions are primitive, then this is the identity mapping. If, on the other hand some shape functions have more than one non-zero vector components, then they may occupy more than one row, and this array indicates which is the first one.

The questions which particular vector component occupies which row for a given shape function is answered as follows: we allocate one row for each non-zero component as indicated by the FiniteElement::get_nonzero_components() function, and the rows are in ascending order exactly those non-zero components.

template<int dim, int spacedim = dim>
UpdateFlags FEValuesData< dim, spacedim >::update_flags

Original update flags handed to the constructor of FEValues.


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

deal.II documentation generated on Mon Nov 23 22:57:44 2009 by doxygen 1.6.1