An optimal compact sixth-order finite difference scheme for the Helmholtz equation |
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| Authors: | Tingting Wu Ruimin Xu |
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| Affiliation: | 1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China;2. School of Science, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China |
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| Abstract: | ![]()
In this paper, we present an optimal compact finite difference scheme for solving the 2D Helmholtz equation. A convergence analysis is given to show that the scheme is sixth-order in accuracy. Based on minimizing the numerical dispersion, a refined optimization rule for choosing the scheme’s weight parameters is proposed. Numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters. |
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| Keywords: | Helmholtz equation Compact finite difference scheme Numerical dispersion |
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