From 7c8035e990affd485b10b92767682cebc68bd4da Mon Sep 17 00:00:00 2001 From: Jean-Paul Pelteret Date: Sun, 2 Jun 2019 21:41:48 +0200 Subject: [PATCH] Write description of AD improvements --- 9.1/paper.tex | 45 +++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 43 insertions(+), 2 deletions(-) diff --git a/9.1/paper.tex b/9.1/paper.tex index 0b5a4ca..2c9edb0 100644 --- a/9.1/paper.tex +++ b/9.1/paper.tex @@ -148,7 +148,7 @@ GNU Lesser General Public License (LGPL). Downloads are available at The major changes of this release are: % \begin{itemize} - \item Improved support for automatic and symbolic differentiation (see + \item Improved support for automatic differentiation (see Section~\ref{subsec:ad}), \item Full support for $hp$ adaptivity in parallel computations (see Section~\ref{subsec:hp}), @@ -261,9 +261,50 @@ in the file that lists all changes for this release}, see \cite{changes91}. the release announcement.) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Improved support for automatic and symbolic differentiation} +\subsection{Improved support for automatic differentiation} \label{subsec:ad} +In the previous release, numerous classes that are used to assemble linear systems +and right hand sides, as well those used to define constitutive laws, were given +full support for ``white-listed'' automatically differentiable (AD) number types +from the ADOL-C and Sacado libraries. +In the current release we have provided a unified interface to these +AD libraries focussing two specific use contexts, namely +\begin{enumerate} +\item the construction and linearization of finite element residuals, and +\item the construction and linearization of constitutive model kinetic variables. +\end{enumerate} + +In the first context, the finite element degrees of freedom are considered the +independent variables. From these primitives, the \texttt{EnergyFunctional} helper +class in the namespace \texttt{Differentiation::AD} may be used to compute both the +residual and its linearization by directly defining the contribution to the +(twice differentiated) scalar total energy functional from each cell. Similarly, +the \texttt{ResidualLinearization} class requires the (once-differentiated) finite +element residual to be defined on a per cell basis, and this contribution is +automatically linearized. + +The second context aims directly at constitutive model formulations, and serves to +compute the directional derivatives of components of (multi-field) constitutive laws +with respect to the scalar, vector, tensor and symmetric tensor fields in terms +of which they are parameterized. The \texttt{ScalarFunction} class may be used to +define a scalar function (such as strain energy function) that may be twice +differentiated, while the \texttt{VectorFunction} may be used to define a vector +function (such as a set of kinematic fields) that may be differentiated once. +Since the total derivatives of all components are computed at once, these two helper +classes provide an interface to retrieve each sub-component of the gradient and +Hessian (for a \texttt{ScalarFunction}) or values and Jacobian (for a +\texttt{VectorFunction}). + +Although these aforementioned helper classes have been documented with a specific +use in mind, they remain generic and may (with a reinterpretation of the meaning of +the independent and dependent variables) be used for other purposes as well. +Furthermore, through the implementation of \texttt{TapedDrivers} and +\texttt{TapelessDrivers} classes that interface with the active AD library, the +generic helper classes hide library-dependent implementational details and facilitate +switching between the supported libraries and AD number types based on the +user's requirements. + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Full support for $hp$ adaptivity in parallel computations} \label{subsec:hp} -- 2.39.5