Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE

被引：3

作者：

Zwicke, Florian ^{[1
]}

Knechtges, Philipp ^{[1
]}

Behr, Marek ^{[1
]}

Elgeti, Stefanie ^{[1
]}

机构：

[1] Rhein Westfal TH Aachen, Chair Computat Anal Tech Syst CATS, Ctr Computat Engn Sci, D-52056 Aachen, Germany

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 11期

关键词：

Automatic differentiation; Newton-Raphson method; Finite element method; LOG-CONFORMATION FORMULATION; CONSTITUTIVE LAWS; DIFFERENTIATION; EFFICIENT; MATRIX; TOOL;

D O I：

10.1016/j.camwa.2016.10.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In an effort to increase the versatility of finite element codes, we explore the possibility of automatically creating the Jacobian matrix necessary for the gradient-based solution of nonlinear systems of equations. Particularly, we aim to assess the feasibility of employing the automatic differentiation tool TAPENADE for this purpose on a large Fortran codebase that is the result of many years of continuous development. As a starting point we will describe the special structure of finite element codes and the implications that this code design carries for an efficient calculation of the Jacobian matrix. We will also propose a first approach towards improving the efficiency of such a method. Finally, we will present a functioning method for the automatic implementation of the Jacobian calculation in a finite element software, but will also point out important shortcomings that will have to be addressed in the future. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：2808 / 2822

页数：15

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