A novel parametric model order reduction approach with applications to geometrically parameterized microwave devices

Abstract

Purpose

The goal is to derive a numerical method for computing parametric reduced-order models (PROMs) from finite-element (FE) models of microwave structures that feature geometrical parameters.

Design/methodology/approach

First, a parameter-dependent FE mesh is constructed by a topology-preserving mesh-morphing algorithm. Then, multivariate polynomial interpolation is employed to achieve explicit geometrical parameterization of all FE matrices. Finally, a PROM based on parameter-dependent projection matrices is constructed by means of interpolation and state transformation techniques.

Findings

The resulting PROMs are of low dimension and fast to evaluate. Moreover, the method features high rates of convergence, and the number of FE solutions required for constructing the PROM is small. The accuracy of the PROM is only limited by that of the underlying FE model and can be controlled by varying the PROM dimension.

Research limitations/implications

Since the method uses topology-preserving mesh-morphing algorithms to instantiate FE models at a number of interpolation points in geometrical parameter space, there are limitations to the amount of deformation that can be handled.

Practical implications

PROM evaluations are computationally cheap. In many cases they can be evaluated hundreds or even thousands of times per second. Therefore, PROMs are very well-suited for parametric studies or numerical optimization.

Originality/value

The presented methodology employs a new way of constructing parameter-dependent interpolation matrices, based on interpolation and space transformations. The proposed methodology yields better accuracy and higher rates of convergence than previous approaches.

Citation

Burgard, S., Farle, O. and Dyczij-Edlinger, R. (2013), "A novel parametric model order reduction approach with applications to geometrically parameterized microwave devices", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 5, pp. 1525-1538. https://doi.org/10.1108/COMPEL-04-2013-0119