Acoustic analysis with absorbing finite elements and far-field computations using free-space Green's functions

Abstract

A family of absorbing-boundary finite elements (FEs) is recently developed for the acoustic time-harmonic, transient and modal analyses of problems having fluid domains of infinite extent. These elements can be easily ‘glued’ to the truncated exterior surface of an underlying FE mesh. The desirable characteristics of the absorbing elements are that they are local and produce banded symmetric element matrices. Since the use of the absorbing FEs reduces the size of the FE model through the premature truncation of the mesh, a post-processing procedure must be employed to obtain solutions far away from FE domain in the case of transient and time-harmonic analyses. In this paper free-space Green's functions are utilized, in the context of time-harmonic analysis, in association with the computed solutions at the exterior boundary where absorbing-boundary FEs are placed in order to compute pressure distribution outside the FE computational domain. The paper demonstrates that the computation of accurate pressure gradients at the absorbing-boundary element nodes plays a crucial role in obtaining accurate pressure solutions outside the FE computational domain.