Druskin, Vladimir and Güttel, Stefan and Knizhnerman, Leonid (2016) Nearoptimal perfectly matched layers for indefinite Helmholtz problems. SIAM Review, 58 (1). pp. 90116. ISSN 10957200
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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 nearbest 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 threeterm 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, NeumanntoDirichlet 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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Nearoptimal perfectly matched layers for indefinite Helmholtz problems. (deposited 05 Nov 2013)

Nearoptimal perfectly matched layers for indefinite Helmholtz problems. (deposited 25 Feb 2014)

Nearoptimal perfectly matched layers for indefinite Helmholtz problems. (deposited 30 Dec 2014)
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Nearoptimal perfectly matched layers for indefinite Helmholtz problems. (deposited 30 Dec 2014)

Nearoptimal perfectly matched layers for indefinite Helmholtz problems. (deposited 25 Feb 2014)
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