A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method

This paper presents a wideband fast multipole boundary element approach for three dimensional acoustic shape sensitivity analysis. The Burton–Miller method is adopted to tackle the fictitious eigenfrequency problem associated with the conventional boundary integral equation method in solving exterior acoustic wave problems. The sensitivity boundary integral equations are obtained by the direct differentiation method, and the concept of material derivative is used in the derivation. The iterative solver generalized minimal residual method (GMRES) and the wideband fast multipole method are employed to improve the overall computational efficiency. Several numerical examples are given to demonstrate the accuracy and efficiency of the present method.

► A wideband fast multipole boundary element approach for 3D acoustic shape sensitivity analysis.
► Boundary integral equations of sensitivity coefficients based on Burton–Miller's method.
► Analytical evaluation of hypersingular integrals for constant element for efficient treatment.
► Demonstrations of accuracy and efficiency of the approach through numerical examples.