Scalable Analysis and Design Using Automatic Differentiation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913869685850112 |
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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 |