THIRD-ORDER DOUBLY ASYMPTOTIC APPROXIMATIONS FOR COMPUTATIONAL ACOUSTICS

Abstract

A fully and symmetrically matched, third-order doubly asymptotic computational boundary (DAA3) is presented in both operator and matrix forms. Its performance is then compared with that of other DAA boundaries for the spherical geometry, which admits an exact series solution. Based on stability, accuracy and passivity as performance criteria, DAA3 is found to be superior to all other DAAs formulated to date. However, there are other third-order forms that are nearly as good, and are easier to implement in boundary-element form. The existence of both DAA2 and DAA3 boundaries enables the analyst to assess solution accuracy for a given problem through the comparison of results produced with these higher approximations of different order.