Reference documentation for deal.II version 9.6.1
 
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
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Differentiation::AD::internal::HessianType< FEValuesExtractors::Scalar, FEValuesExtractors::SymmetricTensor< 2 > > Struct Reference

#include <deal.II/differentiation/ad/ad_helpers.h>

Inheritance diagram for Differentiation::AD::internal::HessianType< FEValuesExtractors::Scalar, FEValuesExtractors::SymmetricTensor< 2 > >:

Public Types

template<int, int dim, typename NumberType>
using type = SymmetricTensor<2 , dim, NumberType>
 
using type
 

Detailed Description

An intermediate helper struct that defines the return type of Hessian (second derivative) calculations of scalar fields with respect to fields defined by the two extractor-type template parameters. This particular specialization is for taking the first derivative with respect to a scalar field, and the second with respect to a symmetric tensor field.

Definition at line 2245 of file ad_helpers.h.

Member Typedef Documentation

◆ type [1/2]

The type associated with computing the gradient of a scalar field with respect to the given ExtractorType_Row = FEValuesExtractors::Scalar followed by the ExtractorType_Col = FEValuesExtractors::SymmetricTensor<2>.

Definition at line 2257 of file ad_helpers.h.

◆ type [2/2]

The type associated with computing the gradient of a scalar field with respect to the given ExtractorType_Row followed by the ExtractorType_Col.

Note
We set the return type for HessianType<FEExtractor::Vector,FEExtractor::Vector> as a normal Tensor. This is because if one has two vector components, the coupling tensor (i.e. Hessian component<FE::V_1,FE::V_2>) is in general not symmetric.

Definition at line 2208 of file ad_helpers.h.


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