Algebraic approach to absorbing boundary conditions for the Helmholtz equation

Abstract

Recent work has shown that designing absorbing boundary conditions through algebraic approaches may be a nice alternative to the continuous approaches based on a Fourier analysis. In this paper, an original algebraic technique based on the computation of small patches is presented for the Helmholtz equation. This new technique is not directly linked to the continuous equations of the problem, nor to the numerical scheme. These properties make this technique very convenient to implement in a domain decomposition context. The proposed algebraic absorbing boundary conditions are used in a non-overlapping domain decomposition method and are defined on the interface between the subdomains. An additional coarse grid correction is then applied to ensure full scalability of the domain decomposition method upon the number of subdomains. This coarse grid correction involves trigonometric functions defined on the interface between the subdomains. Numerical experiments are presented and illustrate the robustness and parallel efficiency of the proposed method for acoustics applications.

Keywords:

• Domain decomposition
• Algebraic patch substructuring
• Coarse grid
• Absorbing boundary condition
• Acoustics