Commun. Comput. Phys., 5 (2009), pp. 442-455.

Fourth Order Schemes for Time-Harmonic Wave Equations with Discontinuous Coefficients

Guy Baruch 1, Gadi Fibich 1, Semyon Tsynkov 2, Eli Turkel 1*

1 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.
2 Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA.

Received 29 July 2007; Accepted (in revised version) 28 August 2007
Available online 1 August 2008


We consider high order methods for the one-dimensional Helmholtz equation and frequency-Maxwell system. We demand that the scheme be higher order even when the coefficients are discontinuous. We discuss the connection between schemes for the second-order scalar Helmholtz equation and the first-order system for the electromagnetic or acoustic applications.

AMS subject classifications: 65N06, 78A48, 78M20

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Key words: Helmholtz equation, Maxwell's equations, finite volume approximation, compact schemes, high order methods, material discontinuities.

*Corresponding author.
Email: (G. Baruch), (G. Fibich), (S. Tsynkov), (E. Turkel)

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