一种分析多频声学问题的等几何边界元法

An isogeometric boundary element method for multi-frequency acoustic problems

将泰勒展开引入等几何边界元法,提出一种应用于三维声学问题的多频计算方法。基本解指数项运用泰勒级数展开,使波数独立于系数方程组。在该方法中,系统矩阵各个元素在多频率计算中仅积分计算一次,可以有效节约奇异和近奇异积分时间。和常规边界积分方程方法分析声学问题比较,该方法可以大量减少CPU计算时间。该等几何方法使用一种局部B样条形函数,可以有效避免在参数曲面映射到实际物理曲面过程中可能产生包含奇异点的几何曲面的问题,进而提高计算精度和计算效率。同时,该等几何方法可以使网格的划分更加便捷。耦合等几何方法,可以使边界元法实现CAD与CAE的无缝连接。数值试验证明,该方法是一种精确有效的多频率计算方法。

A multi-frequency calculation technique based on Taylor series expansion was introduced in the isogeometric boundary element method(IBIEM)for 3 D acoustic problems.The Taylor series expansion was used as the fitting function of the exponential term in fundamental solution,thus,all the entries in system matrices were independent of wave number.The entries in all the matrices(different wave number)only integrated once.Comparing with the original IBEM,the CPU time would be reduced much.A local B spline function was used in this geometric method,which could effectively avoid the singular points problems when mapping the parametric surface to the actual physical surface,and further improve the accuracy and efficiency of computation.At the same time,the geometric method made the mesh more convenient.The coupling isogeometric geometry method made the boundary element method realize the seamless connection between CAD and CAE.Numerical examples indicated the accuracy and efficiency of the presented technique.