Galerkin Method for the Scattering Problem of a Slit

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• 作者：Yujie Wang ; Fuming Ma ; Enxi Zheng
• 关键词：Scattering problem ; Helmholtz equation ; Diffraction ; Dirichlet ; to ; Neumann map ; Galerkin method
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：70
• 期：1
• 页码：192-209
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

In this paper, the scattering problem of a slit is considered. By use of the exact Dirichlet-to-Neumann map and the continuity of the total field on the slit, we reformulate this problem to an operator equation. The well-posedness of the solution is proved. We apply Galerkin method to solve this operator equation numerically and prove the convergence of the numerical solution. Finally some computational examples are presented to show the effectiveness of our method.