用交错施瓦茨法耦合不同区域的简化模型，提升求解效率。
Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method
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本文提出并评估了一种基于域分解的耦合方法，用于将通过非侵入式算子推断（OpInf）构建的子域局部简化模型（ROMs）与子域局部全阶模型（FOMs）进行连接，该方法针对定义在空间几何上的偏微分方程（PDE）实施域分解。通过重叠施瓦茨交替法实现子域模型的耦合，该方法将整体问题转化为一系列子域局部问题，各子域间通过界面传输边界条件进行通信。在提出适用于OpInf ROMs的施瓦茨交替法（称为OpInf-Schwarz）后，我们在二维热方程的多个测试案例上评估了其精度与效率。结果表明，该方法可成功耦合任意组合的OpInf ROMs与FOMs，且在执行OpInf ROM耦合时相较于单体全阶模型可实现加速。实验验证了其在复杂几何和多物理场模拟中的潜力。
原文摘要 · Abstract (English)
This paper presents and evaluates an approach for coupling together subdomain-local reduced order models (ROMs) constructed via non-intrusive operator inference (OpInf) with each other and with subdomain-local full order models (FOMs), following a domain decomposition of the spatial geometry on which a given partial differential equation (PDE) is posed. Joining subdomain-local models is accomplished using the overlapping Schwarz alternating method, a minimally-intrusive multiscale coupling technique that works by transforming a monolithic problem into a sequence of subdomain-local problems, which communicate through transmission boundary conditions imposed on the subdomain interfaces. After formulating the overlapping Schwarz alternating method for OpInf ROMs, termed OpInf-Schwarz, we evaluate the method's accuracy and efficiency on several test cases involving the heat equation in two spatial dimensions. We demonstrate that the method is capable of coupling together arbitrary combinations of OpInf ROMs and FOMs, and that speed-ups over a monolithic FOM are possible when performing OpInf ROM coupling.
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