Three Dimensional Acoustic Shape Sensitivity Analysis by Means of Adjoint Variable Method and Fast Multipole Boundary Element Approach

A fast multipole boundary element approach to the shape sensitivity analysis of three dimensional acoustic wave problems is developed in this study based on the adjoint variable method. The concept of material derivative is employed in the derivation. The Burton-Miller formula which is a linear combination of the conventional and normal derivative boundary integral equations is adopted to cope with the non-uniqueness problem when solving exterior acoustic wave problems. Constant elements are used to discretize the boundary surface so that the strongly- and hyper-singular boundary integrals contained in the formulations can be evaluated explicitly and the numerical process can be performed efficiently. Numerical examples are given to demonstrate the accuracy and efficiency of the present algorithm.