消除声学间接边界元非唯一解的方法的对比研究

Comparison of the methods for eliminating the non-unique solution in acoustic Indirect boundary element method

间接边界元法在求解外域声学问题时面临着解的非唯一性问题,因此需要引入特定的处理方法以保证数值结果的稳定性。间接边界元法在求解大规模声学问题时还面临着计算规模受限问题,快速多极算法是目前克服此问题的常用方法,然而不同的非唯一解处理方法给快速多极算法的适用性和效率带来了不同影响。首先给出基于常值单元离散推导出的无奇异间接边界积分方程,然后将内部阻抗法、内部刚性面法以及混合势等几种常用的非唯一解处理方法引入快速多极间接边界元法,通过数值结果对比得出这些方法对快速多极间接边界元法求解精度和计算效率的影响规律,为发展更准确高效的快速间接边界元法提供了参考。

The indirect boundary element method(IBEM)faces the problem of non-uniqueness in solving exterior acoustic problems,and therefore requires specific processing methods to ensure the stability of numerical results.When solving largescale acoustic problems,the IBEM also faces the problem of limited computational scale,and the fast multipole method(FMM)is a commonly used method to overcome this problem.However,different non-unique solution processing methods have different impacts on the applicability and efficiency of the fast multipole method.To solve the aforementioned issues,the nonsingular indirect boundary integral equations(IBIEs),based on constant elements discretization,are first derived in this paper,and then several non-unique solution problem processing methods are extended into the FMM,such as internal impedance,zero internal normal vibration velocity,and mixing potential.By contrasting numerical results acquired by various methods,the accuracy and computational efficiency of the fast multipole IBEMs are then determined.These conclusions can act as guides for the development of a more efficient fast multipole IBEM.