Modal Element Method for Scattering and Absorbing of Sound by Two-Dimensional Bodies

The modal element method for acoustic scattering from a two-dimensional body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains—the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. In this paper, analysis for two-dimensional scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.