中文摘要：

该文对应用双互易边界元法进行三维声场特征值分析时所用的近似函数进行了研究和讨论。分别以RBF函数、TPS函数和扩展的RBF和TPS函数作为近似函数对一长方体封闭空间声特征值进行了计算。计算结果表明：TPS函数得出的结果与其它函数相比是比较精确的，且收敛速度较快，但高次的TPS函数并没有显示出优势；TPS函数、扩展的TPS函数和RBF函数对于域内点的选取不太敏感。

英文摘要：

This paper is concerned with the approximation functions in the Dual Reciprocity Boundary Element Method （DRBEM） for the three-dimensional acoustic eigenvalue analysis.The functions such as RBF （Radial Basis Functions）, TPS （Thin Plate Spline Functions）, ARBF （Augmented Radial Basis Functions） and ATPS （Augmented Thin Plate Spline Functions） are investigated. The acoustic eigenvalues of a rectangular acoustic cavity are numerically solved with the above functions using the DRBEM. The numerical results show that the TPS functions are suitable for the three-dimensional acoustic eigenvalue analysis due to its accuracy and convergence.However,the high order TPS functions are not superior to the low order ones. The numerical example also demonstrates that the TPS, ARBF and ATPS functions are not sensitive to the selection of the internal nodes.