Design sensitivity analysis of three-dimensional acoustic problems using a fast multipole accelerated indirect BEM

In this paper, the design sensitivity formulations for three-dimensional acoustic problems are presented based on the indirect boundary element method (IBEM). The non-unique solution difficulty of the IBEM in solving exterior acoustic problems is avoided by applying a hybrid combination of single and double layer potentials. In order to accelerate the computational procedure easily, a set of non-singular indirect boundary integral equations (IBIEs) for the acoustic design sensitivity analysis are derived and then the fast multipole method (FMM) is employed to accelerate the matrix-vector products in the IBEM. The method is further extended to the design sensitivity analysis of thin-body acoustic problems above an infinite plane. Numerical examples are given to verify the effectiveness and accuracy of the method, and the simulations of thin-body acoustic problems show its potential in engineering applications.