Dynamic flux surrogate-based partitioned methods for interface problems

• Published in: Computer methods in applied mechanics and engineering 2024-09, Vol.429 (C), p.117115, Article 117115
• Main Authors: Bochev, Pavel, Owen, Justin, Kuberry, Paul, Connors, Jeffrey
• Format: Article
• Language: English
• Subjects: Dynamic mode decomposition (DMD); Interface; Partitioned scheme; Transmission problem
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2024.117115

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. We provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.