期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

求解偏微分方程的一类无网格算法 被引量：2

Meshless Method of Solving Partial Differential Equations
原文传递
导出
摘要 利用径向基函数在Sobolev空间Hk(Ω) (k >n2 )中的插值性质 ,由一类特殊的径向函数构成H1 (Ω)空间中的一组基 ,得到求解偏微分方程边值问题的无网格算法 ,并针对散乱数据的特点 ,给出计算整体稠密度h的算法及如何通过加密节点使h值缩小的一个可行的方法 。 By means of the interpolation property of radial basis functions in H^k(Ω) (k>n/2),a meshless method for solving partial differential equations is derived from a basis of H^1(Ω),which is constructed with a kind of special radial functions.An algorithm of computing the value of global data density h for scattered notes and an effective method to reduce the value of h by increasing the number of notes are also given.Finally some numerical expriments are presented by using Sobolev splines and compactly supported positive definite radial basis functions.
作者 吴孝钿
机构地区 复旦大学数学研究所
出处 《复旦学报（自然科学版）》 CAS CSCD 北大核心 2004年第3期292-299,共8页 Journal of Fudan University：Natural Science
关键词 偏微分方程 无网格算法 正定径向基函数 边值问题 插值 PDE meshless method positive definite radial basis functions
分类号 O241.82 [理学—计算数学]
  • 相关文献

参考文献9

  • 1Maithili S,Kansa E J,Suman G.Application of the multiquadric method for numerical solution of elliptic partial differential equations[J].Applied Mathemathics and Computation,1997,84:275-302.
  • 2Wendland H.Meshless Galerkin approximation using radial basis functions[J].Math Comput,1999,68:1521-1531.
  • 3Wu Zongmin.Compactly supported positive definite radial functions[J].AICM,1995(4):283-292.
  • 4Wu Zongmin.Compactly supported radial functions and the strang-fix condition[J].Applied Mathematics and Computation,1997,84:115-124.
  • 5Wendland H.Piecewise polynomial positive definite and compactly supported radial functions of minimal degree[J].AICM,1994(4):389-396.
  • 6Wendland H.Error estimates for interpolation by compactly suppored radial basis functions of minimal deggee[J].J Approx Theory,1998,93:258-272.
  • 7Schaback R.Error estimates and condition numbers for radial basis function interpolation[J].AICM,1995(3):251-264.
  • 8西阿莱PG 蒋尔雄 曹志浩 郭毓译.有限元法数值分析[M].上海:上海科学技术出版社,1978..
  • 9Bateman H.Highter transcendental functions:VolumeⅡ[M].New York: McGraw-Hill,1953.

同被引文献19

  • 1赵建军,丁建完,周凡利,陈立平.Modelica语言及其多领域统一建模与仿真机理[J].系统仿真学报,2006,18(z2):570-573. 被引量：120
  • 2吴义忠,刘敏,陈立平.多领域物理系统混合建模平台开发[J].计算机辅助设计与图形学学报,2006,18(1):120-124. 被引量：35
  • 3周凡利,陈立平,赵建军,等.时域-空间耦合物理系统多领域统一建模与仿真及偏微分代数混合方程系统的求解[C]//中国力学学会学术大会.北京:中国力学学会,2007:760-760.
  • 4Fritzson P. Introduction to Modeling and Simulation of Technical and Physical Systems with Modelica [M]. New York: Wiley-IEEE Press, 2011.
  • 5Saldamli L, Bachmann B, Wiesmann H, et al. A Framework for Describing and Solving PDE Models in Modelica[C]//Proceedings of the 4th Interna- tional Modetica Conference. Hamburg.. Hamburg University of Technology, 2005 : 113-122.
  • 6Li Zhihua, Zheng Ling, Zhang Huili. Modelling and Simulation of PDE Problems in Modelica[J]. Inter- national Journal of Materials and Structural Integri ty, 2009, 3(4) :318-331.
  • 7Khattak A J, Tirmizi S, Islam S. Application of Meshfree Collocation Method to a Class of Nonlin- ear Partial Differential Equations [J]. Engineering Analysis with Boundary Elements, 2009, 33 (5): 661-667.
  • 8Yao Guangming, Siraj U I. Assessment of Global and Local Meshless Methods Based on Collocation with Radial Basis Functions for Parabolic Partial Differential Equations in Three Dimensions [J]. Engineering Analysis with Boundary Elements, 2012, 36(11) :1640-1648.
  • 9Kamruzzaman M, Sonar T, Lutz T, et al. A New Meshless Collocation Method for Partial Differenti- al Equations [J]. Communications in Numerical Methods in Engineering, 2008, 24 (12): 1617- 1639.
  • 10Lu Benzhuo,Holst M J,Mccammo J A,et al.Poisson-Nernst-Planck equations for simulating bimolecular diffusion-reaction processes I:finite element solutions[J].Journal of Computational Physics,2010,229(19):6979-6994.

引证文献2

二级引证文献3

复旦学报（自然科学版）
2004年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部