Abstract

Large-scale simulations play a crucial role in studying a great variety of complex physical phenomena in many areas of science and engineering. Simulation in such large-scale settings often leads to overwhelming demands on computational resources, and this constitutes the main motivation for model reduction. In this context, the goal is to produce a simpler "reduced-order" model which allows for much faster and cheaper simulation while approximating the original model as accurately as possible. For model reduction in realistically large-scale settings with millions of degrees of freedom, interpolatory model reduction methods have emerged as promising candidates, combining as they do flexibility, scalability, and high fidelity. In its simplest form, interpolatory model reduction involves construction of a reduced-order model whose transfer function interpolates that of the original one at selected interpolation points in the frequency domain along selected input and/or output tangent directions. In this talk, we first review how to construct such an interpolant when interpolation points and tangent directions are specified. Then, we examine the crucial question of how to choose interpolation points and tangent directions so as to meet various desired approximation goals. We answer this question in the context of optimal approximation. We then extend the system interpolation methodology for two broader classes of systems:
i) systems with a generalized coprime factorization such as occurs for second-order systems describing forced vibration, systems with internal delays or other forms of infinite-order resolvable subsystems; and
ii) Systems with a structured dependence on parameters that should be retained in the reduced model.
Several examples from different disciplines will be used to illustrate the theoretical discussion.

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