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关于球面映射三角形插值积分点的评估

发表时间:2012-07-15  浏览量:1511  下载量:749
全部作者: 徐嘉,钟宏志
作者单位: 清华大学土木工程系
摘 要: 讨论一种球面映射得到的三角形内的插值和数值积分点。与一维的切比雪夫点类似,这套点可看作是从二维球面三角形上的等面积坐标点映射到任意平面三角形内得到的。首先在球面三角形边界上取等间距点,再将这些点用等面积坐标线相连,交点即为内部点。通过计算勒贝格常数和积分精度,评估了该套点的插值和积分精度,表明其仍具有改进的空间。
关 键 词: 计算数学;拉格朗日插值多项式;数值积分;球面映射;切比雪夫点
Title: Evaluation on interpolation and numerical integration of points on a triangle mapped from a sphere
Author: XU Jia, ZHONG Hongzhi
Organization: Department of Civil Engineering, Tsinghua University
Abstract: Interpolation and numerical integration based on the points on a triangle mapped from a sphere are discussed in this paper. Analogous to one-dimensional Chebyshev points, this set of points is generated through mapping the spherical triangle in the first octant of a unit sphere to an arbitrary straight-edge plane triangle. On the octant, the boundary points are equally spaced and the interior points are the intersections of curves of equiareal coordinate. The Lebesgue constant is computed and the numerical integration accuracy is evaluated. Results indicate that further improvement of the points is needed to enhance its efficiency and accuracy.
Key words: computational mathematics; Lagrange interpolation polynomial; numerical integration; spherical mapping; Chebyshev points
发表期数: 2012年7月第13期
引用格式: 徐嘉,钟宏志. 关于球面映射三角形插值积分点的评估[J]. 中国科技论文在线精品论文,2012,5(13):1198-1204.
 
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