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

Published online by Cambridge University Press:  20 August 2015

Steven Britt ,
Semyon Tsynkov  and
Eli Turkel
Steven Britt*
Affiliation:
Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA
Semyon Tsynkov*
Affiliation:
Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA
Eli Turkel*
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
*
Email:dsbritt@ncsu.edu
Corresponding author.Email:tsynkov@math.ncsu.edu
Email:turkel@post.tau.ac.il
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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.

Keywords

65N0678A4878M20Helmholtz equationvariable coefficientshigh order accuracycompact finite differences
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 520 - 541
Copyright
Copyright © Global Science Press Limited 2011

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