A semi-analytical and boundary-type meshless method with adjoint variable formulation for acoustic design sensitivity analysis

Abstract

This paper proposes a novel semi-analytical method for the two- and three-dimensional acoustic design sensitivity analysis by combining the Burton–Miller-type singular boundary method (BM-SBM) and the adjoint variable method. The BM-SBM is an accurate, stable and boundary-type meshless approach, and can effectively avoid the fictitious frequency issue in the numerical solutions of exterior acoustic problems due to the introduction of the Burton–Miller formula. The origin intensity factors in the BM-SBM are evaluated by employing the empirical formulas and the subtraction and adding-back technique, which is straightforward, accurate and efficient. Unlike the direct differentiation method, the adjoint variable method can save computation time and computer resources since it avoids computing the gradients of state variables by introducing adjoint state space equations. Compared with the existing methods, the present scheme can be regarded as a competitive alternative of acoustic design sensitivity analysis, due to the aforementioned merits. Three numerical examples are provided to illustrate the effectiveness and accuracy of the developed method.