A discontinuous Galerkin method for acoustic scattering problem with DtN boundary condition

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.

Keywords:

• Obstacle scattering problem
• Helmholtz equation
• spectral method
• discontinuous Galerkin method
• DtN boundary condition

AMS Subject Classifications:

• 65N12
• 78A45

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of the first author was supported by the Fundamental Research Funds for the Central Universities [grant number 3132016110]. The second author was supported by the Natural Science Foundation of China [grant number 11371172]. The third author was supported by the Doctoral Scientific Research Foundation of Liaoning Province [grant number 201501187] and Tian Yuan Special Funds of the National Natural Science Foundation of China [grant number 11526043].