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A Robust Optimal Finite Difference Scheme for the Three-Dimensional Helmholtz Equation
Joint Authors
Cheng, Dongsheng
Chen, Baowen
Chen, Xiangling
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-07-22
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We propose a robust optimal 27-point finite difference scheme for the Helmholtz equation in three-dimensional domain.
In each direction, a special central difference scheme with 27 grid points is developed to approximate the second derivative operator.
The 27 grid points are divided into four groups, and each group is involved in the difference scheme by the manner of weighted combination.
As for the approximation of the zeroth-order term, we use the weighted average of all the 27 points, which are also divided into four groups.
Finally, we obtain the optimal weights by minimizing the numerical dispersion with the least-square method.
In comparison with the rotated difference scheme based on a staggered-grid method, the new scheme is simpler, more practical, and much more robust.
It works efficiently even if the step sizes along different directions are not equal.
However, rotated scheme fails in this situation.
We also present the convergence analysis and dispersion analysis.
Numerical examples demonstrate the effectiveness of the proposed scheme.
American Psychological Association (APA)
Cheng, Dongsheng& Chen, Baowen& Chen, Xiangling. 2019. A Robust Optimal Finite Difference Scheme for the Three-Dimensional Helmholtz Equation. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-13.
https://search.emarefa.net/detail/BIM-1197716
Modern Language Association (MLA)
Cheng, Dongsheng…[et al.]. A Robust Optimal Finite Difference Scheme for the Three-Dimensional Helmholtz Equation. Mathematical Problems in Engineering No. 2019 (2019), pp.1-13.
https://search.emarefa.net/detail/BIM-1197716
American Medical Association (AMA)
Cheng, Dongsheng& Chen, Baowen& Chen, Xiangling. A Robust Optimal Finite Difference Scheme for the Three-Dimensional Helmholtz Equation. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-13.
https://search.emarefa.net/detail/BIM-1197716
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197716