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

## TL;DR

This paper investigates using TAPENADE, an automatic differentiation tool, to generate Jacobian matrices automatically in large, complex finite element codes to enhance their versatility and efficiency.

## Contribution

It demonstrates the feasibility of applying TAPENADE for Jacobian calculation in large Fortran finite element codes and discusses potential improvements and current limitations.

## Key findings

- Successful automatic Jacobian implementation in a finite element code
- Identification of efficiency challenges and structural considerations
- Highlighting future improvements for automatic differentiation in complex codes

## Abstract

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.