Reduced-Order Models of Finite-Element Systems Featuring Shape and Material Parameters

Abstract

Since typical finite-element systems are of high dimension, the analysis of parameter-dependent microwave structures over broad frequency bands tends to be very time-consuming. This issue is addressed by parametric order reduction, which provides a systematic methodology for constructing surrogate models that are cheap to evaluate and feature low and controllable levels of error. This article presents an order reduction technique for finite-element models that depends on the operating frequency and features explicit and implicit parameters for material properties and shape, respectively. It uses polynomial interpolation to resolve implicit parameter dependencies and employs parameter-dependent bases defined on sub-domains of parameter space. The resulting reduced-order models are of very small dimension and preserve the structure and frequency dependency of the original finite-element model. Numerical results demonstrate that the proposed method reduces solution times by several orders of magnitude compared to the underlying finite-element model at very low error.