楔形基无网格法解的存在惟一性

J4 ›› 2010, Vol. 45 ›› Issue (2): 44-49.

楔形基无网格法解的存在惟一性

王志刚秦新强党发宁苏李君

王志刚秦新强苏李君：西安理工大学理学院, 陕西西安 710054; 党发宁：西安理工大学水利水电学院, 陕西西安 710048

收稿日期:2009-08-06 出版日期:2010-02-16 发布日期:2010-03-27
通讯作者: 秦新强(1962-),男,博士,教授,研究方向为微分方程数值解及其应用、计算机图形学与辅助几何设计等.Email: xqqin@xaut.edu.cn
作者简介:王志刚(1981-),男,硕士研究生,研究方向为数值计算与数值软件开发.Email: wzg0620@126.com
基金资助:
国家自然科学基金资助项目(50879069); 陕西省教育厅自然科学研究资助项目(08JK399)

The existence and uniqueness of the solution to meshless methodwith ridge basis functions

WANG Zhi-Gang, QIN Xin-Qiang, SU Li-Jun：School of Sciences, Xi′an University of Technology, Xi′an 710054,Shaanxi， China; DANG Fa-Ning： Institute of Water Resources and Hydroelectric Engineering, Xi′an University of Technology, Xi′an 710048, Shaanxi， China

Received:2009-08-06 Online:2010-02-16 Published:2010-03-27

摘要/Abstract

摘要：

将楔形基函数与配点法结合构造了一种新的无网格法。该方法无需背景积分网格,是一种真正的无网格法。将该方法应用于求解椭圆型方程问题,给出了解的存在惟一性,并通过数值算例验证了该算法的可行性。

关键词: 无网格法;楔形基函数;配点法;解的存在惟一性

Abstract:

A new meshless method is introduced based on ridge basis functions and collocation method. This method is a truly meshless technique without

mesh discretization. The existence and uniqueness of the solution of elliptic equations with the meshless method is given. According to numerical

example and analysis, it is seen that the method is feasible.

Key words: meshless method; ridge basis functions; collocation method; the existence and uniqueness of the solution

王志刚秦新强党发宁苏李君. 楔形基无网格法解的存在惟一性[J]. J4, 2010, 45(2): 44-49.

WANG Zhi-Gang, QIN Xin-Qiang, DANG Fa-Ning, SU Li-Jun. The existence and uniqueness of the solution to meshless methodwith ridge basis functions[J]. J4, 2010, 45(2): 44-49.

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