Dynamic flux surrogate-based partitioned methods for interface problems

• Main Authors: Bochev, Pavel, Owen, Justin, Kuberry, Paul
• Format: Journal Article
• Language: English
• Published: 05-02-2024
• Subjects: Computer Science - Computational Engineering, Finance, and Science; Mathematics - Dynamical Systems
• DOI: 10.48550/arxiv.2402.03560

Partitioned methods for coupled problems rely on data transfers between
subdomains to synchronize the subdomain equations and enable their independent
solution. By treating each subproblem as a separate entity, these methods
enable code reuse, increase concurrency and provide a convenient framework for
plug-and-play multiphysics simulations. However, accuracy and stability of
partitioned methods depends critically on the type of information exchanged
between the subproblems. The exchange mechanisms can vary from minimally
intrusive remap across interfaces to more accurate but also more intrusive and
expensive estimates of the necessary information based on monolithic
formulations of the coupled system. These transfer mechanisms are separated by
accuracy, performance and intrusiveness gaps that tend to limit the scope of
the resulting partitioned methods to specific simulation scenarios. Data-driven
system identification techniques provide an opportunity to close these gaps by
enabling the construction of accurate, computationally efficient and minimally
intrusive data transfer surrogates. This approach shifts the principal
computational burden to an offline phase, leaving the application of the
surrogate as the sole additional cost during the online simulation phase. In
this paper we formulate and demonstrate such a \emph{dynamic flux
surrogate-based} partitioned method for a model advection-diffusion
transmission problem by using Dynamic Mode Decomposition (DMD) to learn the
dynamics of the interface flux from data. The accuracy of the resulting DMD
flux surrogate is comparable to that of a dual Schur complement reconstruction,
yet its application cost is significantly lower. Numerical results confirm the
attractive properties of the new partitioned approach.