  Projection-based model order reduction allows for the parsimonious
representation of full order models (FOMs), typically obtained through the
discretization of certain partial differential equations (PDEs) using
conventional techniques where the discretization may contain a very large
number of degrees of freedom. As a result of this more compact representation,
the resulting projection-based reduced order models (ROMs) can achieve
considerable computational speedups, which are especially useful in real-time
or multi-query analyses. One known deficiency of projection-based ROMs is that
they can suffer from a lack of robustness, stability and accuracy, especially
in the predictive regime, which ultimately limits their useful application.
Another research gap that has prevented the widespread adoption of ROMs within
the modeling and simulation community is the lack of theoretical and
algorithmic foundations necessary for the "plug-and-play" integration of these
models into existing multi-scale and multi-physics frameworks. This paper
describes a new methodology that has the potential to address both of the
aforementioned deficiencies by coupling projection-based ROMs with each other
as well as with conventional FOMs by means of the Schwarz alternating method.
Leveraging recent work that adapted the Schwarz alternating method to enable
consistent and concurrent multi-scale coupling of finite element FOMs in solid
mechanics, we present a new extension of the Schwarz formulation that enables
ROM-FOM and ROM-ROM coupling in nonlinear solid mechanics. In order to maintain
efficiency, we employ hyper-reduction via the Energy-Conserving Sampling and
Weighting approach. We evaluate the proposed coupling approach in the
reproductive as well as in the predictive regime on a canonical test case that
involves the dynamic propagation of a traveling wave in a nonlinear
hyper-elastic material.
