Refinement of a Schur Complement Method for Fluid-Structure Interaction through Reduced Order Modeling
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We present a non-iterative Schur complement method for the solution of a fluid-structure interaction problem, employing projection-based reduced order models (ROMs) on one or both subdomains. The formulation is strongly coupled, using a Lagrange multiplier to represent the interfacial stress, and solving a Schur complement equation allows for the independent solution of the subdomain equations at each time step. The inclusion of ROMs in this scheme provides a more robust framework and makes the technique more computationally appealing. Utilizing the supremizer enrichment technique, we offer detailed investigations into the performance of this method with respect to the use of supremizers and with respect to the basis sizes of the reduced order variables. Results indicate that the ROM-ROM coupled formulation yields results that agree well with the full-order solution in a shorter computational time and with a large reduction in the size of the algebraic system.
