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

Steven Britt, Semyon Tsynkov & Eli Turkel

DOI: 10.4208/cicp.091209.080410s

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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@Article{CiCP-9-520, author = {Steven Britt, Semyon Tsynkov and Eli Turkel}, title = {Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.091209.080410s}, url = {http://global-sci.org/intro/article_detail/cicp/7509.html} }
TY - JOUR T1 - Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes AU - Steven Britt, Semyon Tsynkov & Eli Turkel JO - Communications in Computational Physics VL - 3 SP - 520 EP - 541 PY - 2011 DA - 2011/03 SN - 9 DO - http://doi.org/10.4208/cicp.091209.080410s UR - https://global-sci.org/intro/article_detail/cicp/7509.html KW - AB -

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.

Steven Britt, Semyon Tsynkov and Eli Turkel. (2011). Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes. Communications in Computational Physics. 9 (3). 520-541. doi:10.4208/cicp.091209.080410s
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