Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method
This work addresses the challenge of efficiently simulating complex PDEs by coupling models in computational science, but it is incremental as it applies existing coupling techniques to a specific ROM method.
The paper tackles the problem of coupling subdomain-local reduced order models (ROMs) and full order models (FOMs) for partial differential equations using the overlapping Schwarz alternating method, demonstrating that this approach enables arbitrary combinations and achieves speed-ups over monolithic FOMs in test cases involving the heat equation.
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.