On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle
On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle
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DOI：
10.1109/8.247786
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发表时间：
1993-10
影响因子：
5.7
通讯作者：
R. Graglia
中科院分区：
文献类型：
--
作者：
R. Graglia
给出了由于平面三角形上定义的线性变化源分布而产生的静态和动态势的公式。源的一般线性变化用三个线性基函数表示，每个基函数与三角域的不同顶点相关联。对于静态和动态情况，所考虑的奇异核由 3-D 格林函数及其梯度给出。在静态情况下，以分析方式进行电势评估并给出紧凑形式的结果。在动态情况下，结果以适合数值积分的形式给出。 >
Formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented. The general linear variation of the source is represented in terms of three linear basis functions, each one associated with a different vertex of the triangular domain. The singular kernels considered are given by the 3-D Green's function and its gradient, both for the static and dynamic case. In the static case the evaluation of potentials is performed analytically and compact form results are given. In the dynamic case the results are given in a form suited for numerical integration. >