Multi-parameter polynomial order reduction of linear finite element models

Ortwin Farle, Volker Hill, Pär Ingelström and Romanus Dyczij-Edlinger

Mathematical and Computer Modelling of Dynamical Systems, 2007, vol. 14, issue 5, 421-434

Abstract: In this paper we present a numerically stable method for the model order reduction of finite element (FE) approximations to passive microwave structures parameterized by polynomials in several variables. The proposed method is a projection-based approach using Krylov subspaces and extends the works of Gunupudi etal . (P. Gunupudi, R. Khazaka and M. Nakhla, Analysis of transmission line circuits using multidimensional model reduction techniques , IEEE Trans. Adv. Packaging 25 (2002), pp. 174--180) and Slone etal . (R.D. Slone, R. Lee and J.-F. Lee, Broadband model order reduction of polynomial matrix equations using single-point well-conditioned asymptotic waveform evaluation: derivations and theory , Int. J. Numer. Meth. Eng. 58 (2003), pp. 2325--2342). First, we present the multivariate Krylov space of higher order associated with a parameter-dependent right-hand-side vector and derive a general recursion for generating its basis. Next, we propose an advanced algorithm to compute such basis in a numerically stable way. Finally, we apply the Krylov basis to construct a reduced order model of the moment-matching type. The resulting single-point method requires one matrix factorization only. Numerical examples demonstrate the efficiency and reliability of our approach.

Date: 2007
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DOI: 10.1080/13873950701844220

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