Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes
Steven Britt 1, Semyon Tsynkov 1*, Eli Turkel 21 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.
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