Near-optimal perfectly matched layers for indefinite Helmholtz problems

Druskin, Vladimir and Güttel, Stefan and Knizhnerman, Leonid (2016) Near-optimal perfectly matched layers for indefinite Helmholtz problems. SIAM Review, 58 (1). pp. 90-116. ISSN 1095-7200

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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: Article
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: 11 Apr 2016
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2461

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