A Novel Partitioned Approach for Reduced Order Model -- Finite Element Model (ROM-FEM) and ROM-ROM Coupling

TL;DR

This paper introduces a partitioned coupling method for combining reduced order models (ROMs) with finite element models (FEM) or other ROMs, enabling efficient simulation of coupled problems with reduced computational costs.

Contribution

The paper develops a novel partitioned scheme that couples ROMs with FEM or other ROMs using interface fluxes and dual Schur complements, facilitating independent subdomain solutions.

Findings

Effective ROM-FEM and ROM-ROM coupling demonstrated

Decoupling of subdomain equations via explicit time integration

Reduced computational cost for coupled simulations

Abstract

Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and multiscale applications. In this work, we consider a scenario in which one or more of the "codes" being coupled are projection-based reduced order models (ROMs), introduced to lower the computational cost associated with a particular component. We simulate this scenario by considering a model interface problem that is discretized independently on two non-overlapping subdomains. We then formulate a partitioned scheme for this problem that allows the coupling between a ROM "code" for one of the subdomains with a finite element model (FEM) or ROM "code" for the other subdomain. The ROM "codes" are constructed by performing proper orthogonal decomposition (POD) on a snapshot ensemble to obtain a low-dimensional reduced order basis, followed by a Galerkin projection onto this basis. The ROM and/or FEM "codes" on each subdomain are then coupled using a Lagrange multiplier representing the interface flux. To partition the resulting monolithic problem, we first eliminate the flux through a dual Schur complement. Application of an explicit time integration scheme to the transformed monolithic problem decouples the subdomain equations, allowing their independent solution for the next time step. We show numerical results that demonstrate the proposed method's efficacy in achieving both ROM-FEM and ROM-ROM coupling.