Model order reduction of layered waveguides via rational Krylov fitting

Druskin, Vladimir and Güttel, Stefan and Knizhnerman, Leonid (2021) Model order reduction of layered waveguides via rational Krylov fitting. [MIMS Preprint] (Submitted)

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Network-based data-driven reduced order models have recently emerged as an efficient numerical tool for forward and inverse problems of wave propagation. Currently, this technique is limited to two classes of problems: bounded inhomogeneous domains (with applications in multiscale simulation and imaging) and homogeneous halfspaces (for the solution of exterior forward problems). Here we relax the constant coefficient requirement for the latter by considering reduced order models (ROMs) of unbounded waveguides with layered inclusions, thereby giving rise to efficient discrete perfectly matched layers (PMLs) for nonhomogeneous media. Our approach is based on the solution of a nonlinear rational least squares problem using the RKFIT method [M. Berljafa and S. Güttel, SIAM J. Sci. Comput., 39(5):A2049--A2071, 2017]. We show how the solution of this least squares problem can be converted into an accurate sparse network approximation within a rational Krylov framework. Several numerical experiments are included. They indicate that RKFIT computes PMLs more accurately than previous analytic approaches and even works in regimes where the transfer functions to be approximated are highly irregular due to pronounced scattering resonances. Spectral adaptation effects allow for accurate ROMs with dimensions near or even below the Nyquist limit.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 28 Feb 2021 10:58
Last Modified: 28 Feb 2021 10:58

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