Scalable Analysis and Design Using Automatic Differentiation

Fuente: arXiv
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Main Authors: Andrej, Julian, Kolev, Tzanio, Lazarov, Boyan
Format: Preprint
Published: 2025
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author Andrej, Julian
Kolev, Tzanio
Lazarov, Boyan
author_facet Andrej, Julian
Kolev, Tzanio
Lazarov, Boyan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_00746
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Scalable Analysis and Design Using Automatic Differentiation
Andrej, Julian
Kolev, Tzanio
Lazarov, Boyan
Numerical Analysis
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.
title Scalable Analysis and Design Using Automatic Differentiation
topic Numerical Analysis
url https://arxiv.org/abs/2506.00746