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Partitioned methods allow one to build a simulation capability for coupledproblems by reusing existing single-component codes. In so doing, partitionedmethods can shorten code development and validation times for multiphysics andmultiscale applications. In this work, we consider a scenario in which one ormore of the "codes" being coupled are projection-based reduced order models(ROMs), introduced to lower the computational cost associated with a particularcomponent. We simulate this scenario by considering a model interface problemthat is discretized independently on two non-overlapping subdomains. We thenformulate a partitioned scheme for this problem that allows the couplingbetween 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 byperforming proper orthogonal decomposition (POD) on a snapshot ensemble toobtain a low-dimensional reduced order basis, followed by a Galerkin projectiononto this basis. The ROM and/or FEM "codes" on each subdomain are then coupledusing a Lagrange multiplier representing the interface flux. To partition theresulting monolithic problem, we first eliminate the flux through a dual Schurcomplement. Application of an explicit time integration scheme to thetransformed monolithic problem decouples the subdomain equations, allowingtheir independent solution for the next time step. We show numerical resultsthat demonstrate the proposed method's efficacy in achieving both ROM-FEM andROM-ROM coupling.

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