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2013.53: Near-optimal perfectly matched layers for indefinite Helmholtz problems

2013.53: Vladimir Druskin, Stefan Güttel and Leonid Knizhnerman (2013) Near-optimal perfectly matched layers for indefinite Helmholtz problems.

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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 2000 > 30 Functions of a complex variable
MSC 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MIMS number:2013.53
Deposited By:Stefan Güttel
Deposited On:30 December 2014

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