Commun. Comput. Phys., 9 (2011), pp. 520-541.

Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes

Steven Britt 1, Semyon Tsynkov 1*, Eli Turkel 2

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

Received 9 December 2009; Accepted (in revised version) 8 April 2010
Available online 17 September 2010


In many problems, one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method (e.g., fourth order accurate) to alleviate the points-per-wavelength constraint by reducing the dispersion errors. The variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian coordinates. This renders existing fourth order finite difference methods inapplicable. We develop a new compact scheme that is provably fourth order accurate even for these problems. We present numerical results that corroborate the fourth order convergence rate for several model problems.

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

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Key words: Helmholtz equation, variable coefficients, high order accuracy, compact finite differences.

*Corresponding author.
Email: (S. Britt), (S. Tsynkov), (E. Turkel)

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