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

Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes
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Year:    2011

Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 520–541

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.091209.080410s

Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 520–541

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:   

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