Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity
Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity
复制标题
外推技术在某些具有奇异性的被积函数的多维求积中的应用
DOI：
10.1016/0021-9991(76)90087-5
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发表时间：
1976
影响因子：
4.1
通讯作者：
J. N. Lyness
中科院分区：
文献类型：
--
作者：
J. N. Lyness
许多大规模计算都需要将半径的简单函数与笛卡尔坐标中易于表示的函数的乘积进行数值积分。当使用标准方法时，原点的解析奇异性可能会导致相对昂贵的计算。将已知的渐近展开式应用于这类问题可以大大减少费用或提高精度。文中给出了一组有用的展开。描述了一种基于外推的方法，它导致了一种与Romberg积分相似的方法。这里的重点是应用程序。例如，讨论了理论的重新安排，为面向网格的计算提供了一种技术；并全面描述了数值不稳定的可能影响，如何认识它以及如何缓解它。
Many large scale calculations require the numerical integration of functions that are products of simple functions of a radius with a function readily expressed in cartesian coordinates. The analytic singularity at the origin can cause a relatively expensive calculation when standard methods are employed. The application of known asymptotic expansions to this sort of problem can result in a considerable reduction in expense or increase in accuracy. In this paper, a set of useful expansions are stated. An approach based on extrapolation is described that leads to a method not unlike the Romberg integration. The emphasis here is on applications. For example, the rearrangement of the theory to provide a technique for grid-oriented calculations is discussed; and a full description of the possible effect of numerical instability, how to recognize it and how to alleviate it, is included.