Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE
Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE
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自动实现材料定律：使用 TAPENADE 在有限元代码中进行雅可比计算
DOI：
10.1016/j.camwa.2016.10.010
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Elgeti
中科院分区：
文献类型：
--
作者：
Zwicke;Knechtges;Elgeti
为了增加有限元代码的通用性，我们探索了自动创建基于梯度的非线性方程组求解所需的雅可比矩阵的可能性。特别是，我们的目标是评估的可行性，采用自动微分工具TAPENADE为此目的的大型Fortran代码库，是多年的持续发展的结果。作为一个起点，我们将描述的特殊结构的有限元代码和影响，这种代码设计进行了有效的计算的雅可比矩阵。我们还将提出提高这种方法的效率的第一种方法。最后，我们将提出一个功能的方法在有限元软件中的雅可比计算的自动执行，但也将指出重要的缺点，将不得不在未来解决。
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.