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October 8, 2025Open Access

Scalable Analysis and Design Using Automatic Differentiation

Key Points

The methods demonstrated are effective for large-scale PDE-constrained optimization problems, enabling efficient computation.
Performance was evaluated on non-linear steady-state problems using the open-source MFEM library, proving its scalability.
Automatic differentiation localizes calculations at the integration point level, enhancing both serial and parallel solver capabilities.
The integration of finite element operator decomposition allows for non-intrusive application of differentiation techniques.

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.

Scalable Analysis and Design Using Automatic Differentiation

Key Points

Abstract

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