DerivativeApproximation::SecondDerivative< dim > Class Template Reference

List of all members.

Public Types

typedef Tensor< 2, dim > Derivative
typedef Tensor< 1, dim > ProjectedDerivative

Public Member Functions

template<>
double derivative_norm (const Derivative &d)
template<>
double derivative_norm (const Derivative &d)
template<>
double derivative_norm (const Derivative &d)

Static Public Member Functions

template<class InputVector , int spacedim>
static ProjectedDerivative get_projected_derivative (const FEValues< dim, spacedim > &fe_values, const InputVector &solution, const unsigned int component)
static double derivative_norm (const Derivative &d)
static void symmetrize (Derivative &derivative_tensor)

Static Public Attributes

static const UpdateFlags update_flags

Detailed Description

template<int dim>
class DerivativeApproximation::SecondDerivative< dim >

The following class is used to describe the data needed to compute the finite difference approximation to the second derivatives on a cell. See the general documentation of this class for more information on implementational details.

Author:
Wolfgang Bangerth, 2000

Member Typedef Documentation

template<int dim>
typedef Tensor<2,dim> DerivativeApproximation::SecondDerivative< dim >::Derivative

Declare the data type which holds the derivative described by this class.

template<int dim>
typedef Tensor<1,dim> DerivativeApproximation::SecondDerivative< dim >::ProjectedDerivative

Likewise declare the data type that holds the derivative projected to a certain directions.


Member Function Documentation

template<int dim>
template<class InputVector , int spacedim>
static ProjectedDerivative DerivativeApproximation::SecondDerivative< dim >::get_projected_derivative ( const FEValues< dim, spacedim > &  fe_values,
const InputVector &  solution,
const unsigned int  component 
) [inline, static]

Given an FEValues object initialized to a cell, and a solution vector, extract the desired derivative at the first quadrature point (which is the only one, as we only evaluate the finite element field at the center of each cell).

template<int dim>
static double DerivativeApproximation::SecondDerivative< dim >::derivative_norm ( const Derivative d  )  [static]

Return the norm of the derivative object. Here, for the (symmetric) tensor of second derivatives, we choose the absolute value of the largest eigenvalue, which is the matrix norm associated to the $l_2$ norm of vectors. It is also the largest value of the curvature of the solution.

template<int dim>
static void DerivativeApproximation::SecondDerivative< dim >::symmetrize ( Derivative derivative_tensor  )  [static]

If for the present derivative order, symmetrization of the derivative tensor is necessary, then do so on the argument.

For the second derivatives, each entry of the tensor is set to the mean of its value and the value of the transpose element.

Note that this function actually modifies its argument.

template<>
double DerivativeApproximation::SecondDerivative< 1 >::derivative_norm ( const Derivative d  )  [inline]
template<>
double DerivativeApproximation::SecondDerivative< 2 >::derivative_norm ( const Derivative d  )  [inline]
template<>
double DerivativeApproximation::SecondDerivative< 3 >::derivative_norm ( const Derivative d  )  [inline]

Member Data Documentation

template<int dim>
const UpdateFlags DerivativeApproximation::SecondDerivative< dim >::update_flags [static]

Declare which data fields have to be updated for the function get_projected_derivative to work.


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

deal.II documentation generated on Mon Nov 23 22:57:37 2009 by doxygen 1.6.1