Druskin, Vladimir and Güttel, Stefan and Knizhnerman, Leonid (2016) Compressing variable-coefficient exterior Helmholtz problems via RKFIT. [MIMS Preprint]
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Abstract
The efficient discretization of Helmholtz problems on unbounded domains is a challenging task, in particular, when the wave medium is nonhomogeneous. We present a new numerical approach for compressing finite difference discretizations of such problems, thereby giving rise to efficient perfectly matched layers (PMLs) for nonhomogeneous media. This approach is based on the solution of a nonlinear rational least squares problem using the RKFIT method proposed in [M. Berljafa and S. Guettel, SIAM J. Matrix Anal. Appl., 36(2):894--916, 2015]. We show how the solution of this least squares problem can be converted into an accurate finite difference grid within a rational Krylov framework. Several numerical experiments are included. They indicate that RKFIT computes PMLs more accurate than previous analytic approaches and even works in regimes where the Dirichlet-to-Neumann functions to be approximated are highly irregular. Spectral adaptation effects allow for accurate finite difference grids with point numbers below the Nyquist limit.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | finite difference grid, Helmholtz equation, Dirichlet-to-Neumann map, perfectly matched layer, rational approximation, continued fraction |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 30 Functions of a complex variable MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |
| Depositing User: | Stefan Güttel |
| Date Deposited: | 08 Nov 2016 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2512 |
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Compressing variable-coefficient exterior Helmholtz problems via RKFIT. (deposited 04 Nov 2016)
- Compressing variable-coefficient exterior Helmholtz problems via RKFIT. (deposited 08 Nov 2016) [Currently Displayed]
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