[1]蔡国宪,李炯天,朴光日,等.稀疏网格配置法在随机Burgers’方程中的应用[J].延边大学学报(自然科学版),2014,40(01):20-24.
　CAI Guoxian,LEE Hyungchun,PIAO Guangri,et al.Application of the sparse-grid stochastic collocation method to the stochastic Burgers’ equation[J].Journal of Yanbian University,2014,40(01):20-24.
点击复制

稀疏网格配置法在随机Burgers’方程中的应用

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第40卷 期数: 2014年01期 页码: 20-24 栏目: 基础科学研究 出版日期: 2014-03-20
Title:
Application of the sparse-grid stochastic collocation method to the stochastic Burgers’ equation
作者:
蔡国宪1;  李炯天1;  朴光日2;  金元峰2
1.韩国亚洲大学 数学系, 水原 443-749; 2.延边大学理学院 数学系, 吉林 延吉 133002
Author(s):
CAI Guoxian1;  LEE Hyungchun1;  PIAO Guangri2;  JIN Yuanfeng2
1.Department of Mathematics, Ajou University, Suwon 443-749, Korea; 2.Department of Mathematics, College of Science, Yanbian University, Yanji 133002, China
关键词:
随机配置方法;  稀疏网格配置法;  随机Burgers’方程
Keywords:
stochastic collocation method;  sparse-grid collocation method;  stochastic Burgers’ equation
分类号:
O242.21
文献标志码:
A
摘要:
研究了稀疏网格配置法在随机Burgers’方程中的应用.首先介绍了随机配置方法,并在此基础上引入了稀疏网格配置法,最后通过数值计算结果比较了稀疏网格配置法和蒙特卡罗方法,进而验证了稀疏网格配置法应用于随机Burgers’方程时的可行性和有效性.
Abstract:
We study an application of the sparse-grid stochastic collocation method to the stochastic Burgers’ equation. For this work, stochastic collocation and sparse-grid technique are applied to the problem. To verify an effectiveness and availability of those methods for the stochastic Burgers’ equation, we provide several numerical experiments.

参考文献/References:

[1] Breiman L. Probability[M]. Boston: Addison-Wesley, 1968.
[2] Babuska I M, Nobile F, Tempone R. RAGS: A stochastic collocation method for elliptic partial differential equations with random input data. echnical report[J]. Siam J Numeri Anal, 2007,45(3):1005-1034.
[3] Barthelmann V, Novak E, Ritter K. RAGS: High dimensional polynomial interpolation on sparse grids[J]. Adv Comput Math, 2000,12(4):273-288.
[4] Smolyak S. Interpolation and quadrature formulas for the classes Was and Eas[J]. Soviet Math Dokl, 1963,4:240-243.
[5] Gerstner T, Griebel M. RAGS: Numerical integration using sparse grids[J]. Numer Algorithms, 1998,18(3/4):209-232.
[6] Winckel G. RAGS: Fast Clenshaw-Curtis quadrature[J]. The Mathworks Central File Exchange, 2005.2. http://www.mathworks.com/matlabcentral/files/6911/clencurtom.
[7] Keese A, Matthies H. RAGS: Numerical methods and smolyak quadrature for nonlinear[J]. Partial Differential Equations: Informatikbericht, 2003,5:253-258.
[8] Smolyak S A. RAGS: Quadrature and interpolation formulas for tensor products of certain classes of functions[J]. Soviet Mathematics, 1963,4:240-243.
[9] Bungartz H, Griebel M. Sparse grids[J]. Acta Numerica, 2004,13:147-269.

备注/Memo

收稿日期: 2013-11-26作者简介: 蔡国宪(1977—),男,讲师,研究方向为计算数学.

更新日期/Last Update: 2014-03-20