Dynamic flux surrogate-based partitioned methods for interface problems

Abstract: 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.