Volume 26, Issue 1
Compact Fourth-Order Finite Difference Schemes for Helmholtz Equation with High Wave Numbers
DOI:

J. Comp. Math., 26 (2008), pp. 98-111

Published online: 2008-02

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• Abstract

In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term, namely, the $\mathcal O(h^4)$ term, is independent of the wave number and the solution of the Helmholtz equation. The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered. Numerical results are presented, which support our theoretical predictions.

• Keywords

Helmholtz equation Compact difference scheme FFT algorithm Convergence

65M06 65N12.

@Article{JCM-26-98, author = {}, title = {Compact Fourth-Order Finite Difference Schemes for Helmholtz Equation with High Wave Numbers}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {1}, pages = {98--111}, abstract = { In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term, namely, the $\mathcal O(h^4)$ term, is independent of the wave number and the solution of the Helmholtz equation. The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered. Numerical results are presented, which support our theoretical predictions.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8613.html} }
TY - JOUR T1 - Compact Fourth-Order Finite Difference Schemes for Helmholtz Equation with High Wave Numbers JO - Journal of Computational Mathematics VL - 1 SP - 98 EP - 111 PY - 2008 DA - 2008/02 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8613.html KW - Helmholtz equation KW - Compact difference scheme KW - FFT algorithm KW - Convergence AB - In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term, namely, the $\mathcal O(h^4)$ term, is independent of the wave number and the solution of the Helmholtz equation. The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered. Numerical results are presented, which support our theoretical predictions.