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Rational approximation recently emerged as an efficient numerical tool forthe solution of exterior wave propagation problems. Currently, this techniqueis limited to wave media which are invariant along the main propagationdirection. We propose a new model order reduction-based approach forcompressing unbounded waveguides with layered inclusions. It is based on thesolution of a nonlinear rational least squares problem using the RKFIT method.We show that approximants can be converted into an accurate finite differencerepresentation within a rational Krylov framework. Numerical experimentsindicate that RKFIT computes more accurate grids than previous analyticapproaches and even works in the presence of pronounced scattering resonances.Spectral adaptation effects allow for finite difference grids with dimensionsnear or even below the Nyquist limit.

Model order reduction of layered waveguides via rational Krylov fitting