Partitioned Scheme for Coupling Heterogenous Numerical Methods, Including Reduced Order Models, Over Nonoverlapping Interfaces
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Creating a digital twin for a physical system often requires multi-scale, multi-physics, and multi-fidelity modeling. However, simulation of individual components of a system are often done using specialized software designed with a particular set of physics in mind and need to be coupled together for multiple components. Additionally, either through the identification of candidates for reduced order modeling (ROM) or machine learned models (ML), or in the absence of a physical model such as a data-driven surrogate, it then becomes necessary to couple non-traditional numerical methods together or with other traditional numerical methods such as the finite element method (FEM). In this talk we present work on a new method for coupling FEM-to-FEM, FEM-to-ROM, and ROM-to-ROM methods using a Lagrange Multiplier (LM) along with a dual-Schur complement. The discussion will cover formulation of the coupling scheme as well as details regarding the construction of LM spaces that lead to a non-singular Schur complement system. Numerical results will be presented demonstrating the accuracy, stability, and conditioning of the approach.
