  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.
