Schwarz Christoffel变换数值解法

doi:10.6040/j.issn.1671-9352.0.2015.152

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (4): 104-111.doi: 10.6040/j.issn.1671-9352.0.2015.152

Schwarz Christoffel变换数值解法

崔建斌¹,姬安召²,鲁洪江³,王玉风²,何姜毅²,许泰²

1. 陇东学院数学与统计学院, 甘肃庆阳 745000;2. 陇东学院能源工程学院, 甘肃庆阳 745000;3. 成都理工大学能源工程学院, 四川成都 610059

收稿日期:2015-04-14 出版日期:2016-04-20 发布日期:2016-04-08
作者简介:崔建斌(1972— ),男,硕士,副教授,研究方向为数据挖掘与灰色预测.E-mail:cuijb0658@163.com
基金资助:
庆阳市科技支撑计划项目(KG201307);陇东学院青年科技创新项目(XYGK1307)

Numerical solution of Schwarz Christoffel transform

CUI Jian-bin¹, JI An-zhao², LU Hong-jiang³, WANG Yu-feng², HE Jiang-yi², XU Tai²

1. Mathematics and Statistics Institute, Longdong University, Qingyang 745000, Gansu, China;
2. Energy Engineering Institute, Longdong University, Qingyang 745000, Gansu, China;
3. Energy Engineering Institute, Chengdu University of Technology, Chengdu 610059, Sichuan, China

Received:2015-04-14 Online:2016-04-20 Published:2016-04-08

摘要/Abstract

摘要： Schwarz Christoffel变换技术在某些工程问题处理中有着重要作用。本文研究Schwarz Christoffel变换方法及其所涉及的数值解法,采用Levenberg-Marquardt算法求解Schwarz Christoffel变换参数的非线性系统。为了提高数值计算精度,对于Schwarz Christoffel变换中出现的奇异积分问题,通过搜寻区间奇异点,细分积分区间,在子区间中采用高斯雅克比型积分,并对其权函数正交多项式零点和权值进行校正。最后给出算例验证了该方法的可行性。

关键词: 奇异积分, 非线性方程组, Schwarz Christoffel变换, 高斯雅克比型积分, Levenberg-Marquardt算法

Abstract: Schwarz Christoffel transformation technique has an important role to deal with engineering problem. Schwarz Christoffel transformation and its reference to numerical solution are studied.The nonlinear system of Schwarz Christoffel transform parameters is solved using Levenberg-Marquardt algorithm about. To increase the numerical accuracy, for the Singular Integral problem occurred during the course of Schwarz Christoffel transformation, search the interval singularity and sub-divide interval, which is to correct weight function and Zeros of Orthogonal Polynomials by Gauss-Jacobi quadrature in subdivide interval. Finally an example is given and the method feasible is verified.

Key words: Gauss-Jacobi quadrature, nonlinear equations, Schwarz Christoffel transform, singular integral, Levenberg-Marquardt algorithm

中图分类号:

O241

崔建斌,姬安召,鲁洪江,王玉风,何姜毅,许泰. Schwarz Christoffel变换数值解法[J]. 山东大学学报（理学版）, 2016, 51(4): 104-111.

CUI Jian-bin, JI An-zhao, LU Hong-jiang, WANG Yu-feng, HE Jiang-yi, XU Tai. Numerical solution of Schwarz Christoffel transform[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 104-111.

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Schwarz Christoffel变换数值解法

Numerical solution of Schwarz Christoffel transform

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