A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions

Abstract

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Generalized Method of Moments: A novel framework for analyzing acoustic scattering from complex objects using a locally smooth surface parametrization and adaptive basis spaces

“…Boundary integral formulations offer an efficient modality for the analysis of fields scattered by homogeneous objects as (i) they can be formulated only in terms of surface integral equations and (ii) radiation boundary conditions are explicitly included in the Green's function. Despite their advantages, their formulation is more difficult than that of their differential equation counterparts, and as a result this method has seen sporadic development in the past 10,11 , and a more concerted effort recently 12,13,14,15,16,17,18,19 . The recent development of fast solvers that ameliorate the CPU and memory complexity of surface integral equation based solvers, i.e., reduce the scaling from O(N 2 s ) to O(N s log 2 N s ) where N s is the number of spatial degrees of freedom, has made these techniques more appealing 20,21 .…”

Generalized Method of Moments

“…Boundary integral formulations offer an efficient modality for the analysis of fields scattered by homogeneous objects as (i) they can be formulated only in terms of surface integral equations and (ii) radiation boundary conditions are explicitly included in the Green's function. Despite their advantages, their formulation is more difficult than that of their differential equation counterparts, and as a result this method has seen sporadic development in the past 10, 11 , and a more concerted effort recently 12,13,14,15,16,17,18,19 . The recent development of fast solvers that ameliorate the CPU and memory complexity of surface integral equation based solvers, i.e., reduce the scaling from O(N 2 s ) to O(N s log 2 N s ) where N s is the number of spatial degrees of freedom, has made these techniques more appealing 20,21 .…”