  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.
