基于自适应交叉近似边界元法的快速声学灵敏度分析

摘要

基于自适应交叉近似边界元法构造一组快速声学灵敏度分析方法，其中，声学灵敏度分析分别采用直接微分法和伴随变量法；而自适应交叉近似算法被用以克服常规边界元法的高计算量和高存储量的固有缺点。自适应交叉近似算法在迭代求解之前对边界元系数矩阵进行压缩存储，可以在降低存储量的同时提高求解效率。在声学灵敏度分析中，通过直接使用求解未知边界状态值时保存的压缩系数矩阵，可以进一步提高求解效率。数值算例验证了所构造的方法的计算精度和求解效率，以及在大规模声场问题的最优化分析中的应用潜力。%A set of fast acoustic design sensitivity analysis approaches are developed in this paper based on the boundary element method accelerated by the adaptive cross approximation (ACA ) .Both the direct differentiation method and the adjoint variable method are implemented in the design sensitivity analysis . Since the compressed coefficient matrices can be obtained in the ACA before the iterative solution proce-dure ,the ACA can be adopted to conquer not only the high storage requirement but also the high compu-tational cost of the conventional boundary element method .Moreover ,the compressed matrices are re-used in the acoustic design sensitivity analysis in order to make the developed approaches more efficient . Numerical examples are used to demonstrate the accuracy and efficiency of the developed approaches ,and also the potential in large-scale acoustic optimization problems .