边界元特征值分析及Burton-Miller法探究  

BEM eigenvalue analysis and the investigation of the Burton-Miller method

作　　者：郑昌军[1] 高海峰[2] 杜磊[3] 陈海波[4] 

机构地区：[1]合肥工业大学噪声振动工程研究所,合肥230009 [2]太原理工大学力学学院,太原030024 [3]大连理工大学数学科学学院,大连116024 [4]中国科学技术大学近代力学系,合肥230027

出　　处：《计算力学学报》2016年第3期335-342,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11172291;11402071)资助项目

摘　　要：运用围道积分方法将边界元非线性特征值问题转化为规模很小的广义特征值问题,从而构造出一种边界元特征值分析方法。数值算例验证了该方法的求解精度。针对外声场问题,通过对常规、法向导数和BurtonMiller边界积分方程的虚假特征频率的计算和比较,揭示了Burton-Miller法规避虚假特征频率的本质,并对其中的叠加常数的最优取值给出了一种新的解释。A boundary element eigenvalue analysis method is developed with a contour integral method which is used to convert the boundary element nonlinear eigenvalue problems into small generalized eigenvalue problems. Numerical examples are utilized to demonstrate the accuracy of the developed method. Fictitious eigenfrequency phenomena of the conventional boundary integral equation,its normal derivative formulation and the Burton-Miller formulation are investigated through exterior acoustic examples. The actual effect of the Burton-Miller formulation on the fictitious eigenfrequency problems is revealed and the optimal choice of the coupling parameter is confirmed.

关 键 词：边界元法 虚假特征频率 Burton-Miller法 叠加常数 围道积分方法 

分 类 号：O242.2[理学—计算数学]