Volume 9, Issue 3
Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes

Steven Britt, Semyon Tsynkov & Eli Turkel

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

Published online: 2011-03

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  • Abstract

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.

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COPYRIGHT: © Global Science Press

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