3-D acoustic shape sensitivity analysis using the fast multipole boundary element method

The fast multipole boundary element method (FMBEM), based on the Burton Miller formulation for 3-D acoustic sensitivity analysis, is presented in this paper in order to overcome the difficulties in the shape sensitivity analyses using the boundary element method based on the direct differentiation method. The Burton-Miller formulation, which is a linear combination of the conventional boundary integral equation (CBIE) and its normal derivative (NDBIE), is applied to circumvent the difficulty caused by the so-called fictitious eigen-frequencies. The fast multipole method (FMM) is also employed to improve the overall computational efficiency. The sensitivity boundary integral equations of hypersingular type are obtained by the direct differentiation method. The correctness and validity of the method are demonstrated through some numerical results, from which the effectiveness of the present method is shown for 3-D acoustic shape sensitivity analyses.