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This paper formulates, analyzes, and demonstrates numerically a method forthe partitioned solution of coupled interface problems involving combinationsof projection-based reduced order models (ROM) and/or full order methods(FOMs). The method builds on the partitioned scheme developed in [1], whichstarts from a well-posed formulation of the coupled interface problem and usesits dual Schur complement to obtain an approximation of the interface flux.Explicit time integration of this problem decouples its subdomain equations andenables their independent solution on each subdomain. Extension of thispartitioned scheme to coupled ROM-ROM or ROM-FOM problems required formulationswith non-singular Schur complements. To obtain these problems, we project awell-posed coupled FOM-FOM problem onto a composite reduced basis comprisingseparate sets of basis vectors for the interface and interior variables, anduse the interface reduced basis as a Lagrange multiplier. Our analysis confirmsthat the resulting coupled ROM-ROM and ROM-FOM problems have provablynon-singular Schur complements, independent of the mesh size and the reducedbasis size. In the ROM-FOM case, analysis shows that one can also use theinterface FOM space as a Lagrange multiplier. We illustrate the theoretical andcomputational properties of the partitioned scheme through reproductive andpredictive tests for a model advection-diffusion transmission problem.

Explicit synchronous partitioned scheme for coupled reduced order models based on composite reduced bases