四维/六维超立方体中等精度对称求积公式

Moderate Degree Symmetric Quadrature Formulae for Four/Six Dimensional Hypercubes

将Lyness高维超立方体对称求积公式制订规则应用于四维、六维情形,得出了具有9次和11次精度四维超立方体对称求积公式W5(4)和W6(4),以及具有9次和11次精度六维超立方体对称求积公式W5(6)*和W6(6)*。相对于同等精度高斯求积公式,它们具有更少的函数求值次数,求值次数最低可低至185和505次,以及465和1825次。将导出的四维、六维求积公式分别应用于任意导体面目标RWG基伽略金矩量法阻抗元素计算以及非均匀介质目标扩展RWG伽略金矩量法阻抗元素的计算中,计算结果表明在剖分单元电尺寸不超过λ/4的常规应用下,两组四维空间求积公式相对精度在1e-6量级,两组六维空间求积公式求积精度在1e-4量级,求积效果理想。

The Lyness＇ s theory on construction high dimesional sysmetric integration rules is applied to four- and sixdimensional cases. The 9th and l lth degree symmetric quadrature formulae W5^（4） and W6^（4） for four-dimensional hypercubs, and the 9th and llth degree symmetric quadrature formulae W5^（6）＊ and W6^（6）＊ for six-dimensional hypercubs is deduced. Compared to the same degree Gaussian quadrature formulae, these formulae need much less function evaluations. The number of function evaluations of W5^（4） and W5^（4） are 185 and 505, and the number of function evaluations of W5^（6）＊ and W6^（6）＊ are 465 and 1825 respectively. The deduced four- and six- dimensional formulae are used respectively in calculating impedance elements of RWG Galerkin moment method for arbitrary conducting surface objects and extensive RWG Galerkin moment method for inhomogeneous dielectric objects. The calculated results show that when the mesh cells＇ electrical length is less than A/4 , the quardrature relative precision of formulae W5^（4） and W5^（4） are about le-6 for four dimensional, while that of formulae W5^（6）＊ and W6^（6）＊ are about le-4 for six dimensional.