Scalable Analysis and Design Using Automatic Differentiation
Abstract
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to localize the application of AD at the integration point level by combining it with the so-called Finite Element Operator Decomposition. The proposed methods are computationally effective, scalable, automatic, and non-intrusive, making them ideal for existing serial and parallel solvers and complex multiphysics applications. The performance is demonstrated on large-scale steady-state non-linear scalar problems. The chosen testbed, the MFEM library, is free and open-source finite element discretization library with proven scalability to thousands of parallel processes and state-of-the-art high-order discretization techniques.
Cite
@article{arxiv.2506.00746,
title = {Scalable Analysis and Design Using Automatic Differentiation},
author = {Julian Andrej and Tzanio Kolev and Boyan Lazarov},
journal= {arXiv preprint arXiv:2506.00746},
year = {2025}
}