Druskin, Vladimir and Güttel, Stefan and Knizhnerman, Leonid (2013) Near-optimal perfectly matched layers for indefinite Helmholtz problems. [MIMS Preprint]
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Abstract
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the union of a negative and positive real interval, designed with the help of a classical result by Zolotarev. Using Krein's interpretation of a Stieltjes continued fraction, this interpolant can be converted into a three-term finite difference discretization of a perfectly matched layer (PML) which converges exponentially fast in the number of grid points. The convergence rate is asymptotically optimal for both propagative and evanescent wave modes. Several numerical experiments and illustrations are included.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | Helmholtz equation, Neumann-to-Dirichlet map, perfectly matched layer, rational approximation, Zolotarev problem, 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: | 05 Nov 2013 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2039 |
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