Reference documentation for deal.II version GIT 9c182271f7 2023-03-28 14:30:01+00:00
DerivativeApproximation::internal::Gradient< dim > Class Template Reference

## Public Types

using Derivative = Tensor< 1, dim >

using ProjectedDerivative = Tensor< 0, dim >

## 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 = update_values

## Detailed Description

### template<int dim> class DerivativeApproximation::internal::Gradient< dim >

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

Definition at line 80 of file derivative_approximation.cc.

## ◆ Derivative

template<int dim>
 using DerivativeApproximation::internal::Gradient< dim >::Derivative = Tensor<1, dim>

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

Definition at line 93 of file derivative_approximation.cc.

## ◆ ProjectedDerivative

template<int dim>
 using DerivativeApproximation::internal::Gradient< dim >::ProjectedDerivative = Tensor<0, dim>

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

Definition at line 99 of file derivative_approximation.cc.

## ◆ get_projected_derivative()

template<int dim>
template<class InputVector , int spacedim>
 Gradient< dim >::ProjectedDerivative DerivativeApproximation::internal::Gradient< dim >::get_projected_derivative ( const FEValues< dim, spacedim > & fe_values, const InputVector & solution, const unsigned int component )
inlinestatic

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).

Definition at line 139 of file derivative_approximation.cc.

## ◆ derivative_norm()

template<int dim>
 double DerivativeApproximation::internal::Gradient< dim >::derivative_norm ( const Derivative & d )
inlinestatic

Return the norm of the derivative object. Here, for the gradient, we choose the Euclidean norm of the gradient vector.

Definition at line 165 of file derivative_approximation.cc.

## ◆ symmetrize()

template<int dim>
 void DerivativeApproximation::internal::Gradient< dim >::symmetrize ( Derivative & derivative_tensor )
inlinestatic

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

For the first derivatives, no such thing is necessary, so this function is a no-op.

Definition at line 177 of file derivative_approximation.cc.

## ◆ update_flags

template<int dim>
 const UpdateFlags DerivativeApproximation::internal::Gradient< dim >::update_flags = update_values
static

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

Definition at line 87 of file derivative_approximation.cc.

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