Shape design sensitivity analysis of acoustic problems using a boundary element method

Abstract

A boundary integral equation for shape design sensitivity analysis of acoustic problems is presented. In the derivation of the sensitivity equation, the material derivative concept is used. To remove the singularitiess that appear in the conventional sensitivity equation, an integral identity which represents the one-dimensional wave propagation is used. Since the sensitivity equation is regularized, one can obtain the accurate solution using the standard Gaussian scheme. The equation is verified for the pulsating sphere example where an analytical solution is available. The boundary was discretized by a six-node triangular element. As a result, one can obtain the accurate sensitivities of acoustic pressure not only on the boundary but also at the given field points.