A discontinuous Galerkin method for acoustic scattering problem with DtN boundary condition. Issue 6 (26th April 2018)

• Record Type: Journal Article
• Authors: Wang, Yujie; Ma, Fuming; Zheng, Enxi
• Is Part Of: Applicable analysis. Volume 97:Issue 6(2018)
• Page Start: 938
• Page End: 961
• Publication Date: 2018-04-26
• Subjects: Obstacle scattering problem -- Helmholtz equation -- spectral method -- discontinuous Galerkin method -- DtN boundary condition; 65N12 -- 78A45; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1295448
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: This paper is concerned with the scattering problem of time-harmonic acoustic waves by a bounded, sound soft obstacle in two dimensions. We apply the exact Dirichlet-to-Neumann map on the boundary to reformulate this exterior problem into a bounded domain. To cope with this boundary condition the spectral expansion method is used. Because the computational domain does not always satisfy the requirement of spectral method, we couple the DG method and spectral method to solve this problem. DG-norm and -norm error analysis is given explicitly with wave number k . Numerical experiments are also presented to show the effectiveness of our method.