Numerical stabilities study of a decomposed compact method for highly oscillatory Helmholtz equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:354

Article; Proceedings Paper

Jones, Tiffany^1,2  Sheng, Qin^1,2 

[1] Baylor Univ, Dept Math, One Bear Pl, Waco, TX 76798 USA

[2] Baylor Univ, Ctr Astrophys Space Phys & Engn Res, One Bear Pl, Waco, TX 76798 USA

关键词: Wave equation;    High oscillations;    Compact schemes;    Decomposition;    Asymptotic stability;    Self-focusing phenomenon;   

DOI  :  10.1016/j.cam.2018.03.031

来源: Elsevier

【 摘 要 】

This paper concerns numerical stabilities of a decomposed compact finite difference method for solving Helmholtz partial differential equation problems with large wave numbers. Radially symmetric transverse fields and standard polar coordinates are considered. A decomposition is implemented to remove the anticipated singularity in the transverse direction. Compact scheme structures are introduced in the transverse direction to raise the accuracy for laser and subwavelength optical computations. It is proven that, while the highly accurate compact algorithm shies away from the conventional stability in the von Neumann sense, it is asymptotically stable with index one. Additionally, a discussion on theoretical and numerical stabilities for this method is presented. Numerical experiments further demonstrate the high reliability of the scheme when implemented in highly oscillatory optical self-focusing wave propagation simulations. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free