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.

翻译：耦合问题的分区方法依赖于子域间的数据传输来同步子域方程并支持其独立求解。通过将每个子问题视为独立实体，这些方法能够实现代码复用、提升并行性，并为即插即用的多物理场模拟提供便捷框架。然而，分区方法的精度和稳定性关键取决于子问题间交换的信息类型。交换机制可从最小侵入性的跨界面重映射，到基于耦合系统整体公式的更精确但侵入性和计算成本更高的必要信息估计，形式多样。这些交换机制在精度、性能和侵入性方面存在差异，往往使得所得分区方法的适用范围局限于特定模拟场景。数据驱动的系统辨识技术可通过构建精确、计算高效且最小侵入性的数据传输代理，为弥合这些差距提供契机。该方法将主要计算负担转移至离线阶段，使代理应用成为在线模拟阶段唯一的额外成本。本文针对模型对流扩散传输问题，基于动态模态分解（DMD）从数据中学习界面通量动力学，提出并验证了一种基于动态通量代理的分区方法。所得DMD通量代理的精度与对偶Schur补重构方法相当，但其应用成本显著降低。数值结果验证了该新分区方法的优良特性。