Reference documentation for deal.II version Git 1c2f3d7ba8 2021-05-16 10:03:46 +0200
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
Public Types | List of all members
Differentiation::AD::internal::HessianType< ExtractorType_Row, ExtractorType_Col > Struct Template Reference

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

Public Types

template<int rank, int dim, typename NumberType >
using type = Tensor< rank, dim, NumberType >

Detailed Description

template<typename ExtractorType_Row, typename ExtractorType_Col>
struct Differentiation::AD::internal::HessianType< ExtractorType_Row, ExtractorType_Col >

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. The first, ExtractorType_Row, defines the field that the first derivatives are taken with respect to while the second, ExtractorType_Col, defines the field that the second derivatives are taken with respect to.

Definition at line 2196 of file ad_helpers.h.

Member Typedef Documentation

◆ type

template<typename ExtractorType_Row , typename ExtractorType_Col >
template<int rank, int dim, typename NumberType >
using Differentiation::AD::internal::HessianType< ExtractorType_Row, ExtractorType_Col >::type = Tensor<rank, dim, NumberType>

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

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 2210 of file ad_helpers.h.

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