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Projection-based model order reduction allows for the parsimoniousrepresentation of full order models (FOMs), typically obtained through thediscretization of certain partial differential equations (PDEs) usingconventional techniques where the discretization may contain a very largenumber of degrees of freedom. As a result of this more compact representation,the resulting projection-based reduced order models (ROMs) can achieveconsiderable computational speedups, which are especially useful in real-timeor multi-query analyses. One known deficiency of projection-based ROMs is thatthey can suffer from a lack of robustness, stability and accuracy, especiallyin the predictive regime, which ultimately limits their useful application.Another research gap that has prevented the widespread adoption of ROMs withinthe modeling and simulation community is the lack of theoretical andalgorithmic foundations necessary for the "plug-and-play" integration of thesemodels into existing multi-scale and multi-physics frameworks. This paperdescribes a new methodology that has the potential to address both of theaforementioned deficiencies by coupling projection-based ROMs with each otheras well as with conventional FOMs by means of the Schwarz alternating method.Leveraging recent work that adapted the Schwarz alternating method to enableconsistent and concurrent multi-scale coupling of finite element FOMs in solidmechanics, we present a new extension of the Schwarz formulation that enablesROM-FOM and ROM-ROM coupling in nonlinear solid mechanics. In order to maintainefficiency, we employ hyper-reduction via the Energy-Conserving Sampling andWeighting approach. We evaluate the proposed coupling approach in thereproductive as well as in the predictive regime on a canonical test case thatinvolves the dynamic propagation of a traveling wave in a nonlinearhyper-elastic material.

The Schwarz alternating method for the seamless coupling of nonlinear reduced order models and full order models