Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method

TL;DR

This paper introduces OpInf-Schwarz, a minimally-intrusive domain decomposition method for coupling local reduced order models and full order models, improving computational efficiency for PDE simulations.

Contribution

It develops and evaluates a novel Schwarz alternating method for coupling non-intrusive operator inference ROMs with FOMs in a domain decomposition framework.

Findings

The method accurately couples OpInf ROMs and FOMs.

Speed-ups are achieved over monolithic FOM simulations.

The approach is effective for heat equation test cases.

Abstract

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.