An Extended Krylov Subspace Model-Order Reduction Technique to Simulate Wave Propagation in Unbounded Domains

Abstract

In this paper we present a novel extended Krylov subspace reduced-order modeling technique to efficiently simulate time- and frequency-domain wavefields in open complex structures. To simulate the extension to infinity, we use an optimal complex-scaling method which is equivalent to an optimized perfectly matched layer in which the frequency is fixed. Wavefields propagating in strongly inhomogeneous open domains can now be modeled as a non-entire function of the complex-scaled wave operator. Since this function contains a square root singularity, we apply an extended Krylov subspace technique to construct fast converging reduced-order models. Specifically, we use a modified version of the extended Krylov subspace algorithm as proposed by Jagels and Reichel [Linear Algebra Appl., Vol. 434, pp. 1716 - 1732, 2011], since this algorithm allows us to balance the computational costs associated with computing powers of the wave operator and its inverse. Numerical experiments from electromagnetics and acoustics illustrate the performance of the method.