Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed
文献类型：期刊论文
| 作者 | Tang, Tao1; Zhou, Tao2
|
| 刊名 | COMMUNICATIONS IN COMPUTATIONAL PHYSICS
 |
| 出版日期 | 2010-07-01 |
| 卷号 | 8期号:1页码:226-248 |
| ISSN号 | 1815-2406 |
| 关键词 | Hyperbolic equation stochastic collocation methods convergence analysis |
| DOI | 10.4208/cicp.060109.130110a |
| 英文摘要 | For a simple model of a scalar wave equation with a random wave speed, Gottlieb and Xiu [Commun. Comput. Phys., 3 (2008), pp. 505-518] employed the generalized polynomial chaos (gPC) method and demonstrated that when uncertainty causes the change of characteristic directions, the resulting deterministic system of equations is a symmetric hyperbolic system with both positive and negative eigen-values. Consequently, a consistent method of imposing the boundary conditions is proposed and its convergence is established under the assumption that the expansion coefficients decay fast asymptotically. In this work, we investigate stochastic collocation methods for the same type of scalar wave equation with random wave speed. It will be demonstrated that the rate of convergence depends on the regularity of the solutions; and the regularity is determined by the random wave speed and the initial and boundary data. Numerical examples are presented to support the analysis and also to show the sharpness of the assumptions on the relationship between the random wave speed and the initial and boundary data. An accuracy enhancement technique is investigated following the multi-element collocation method proposed by Foo, Wan and Karniadakis [J. Comput. Phys., 227 (2008), pp. 9572-9595]. |
| 资助项目 | Hong Kong Research Grant Council CERG ; Hong Kong Baptist University FRG ; Natural Science Foundation of China[G10729101] |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| 出版者 | GLOBAL SCIENCE PRESS |
| WOS记录号 | WOS:000278713500009 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/10938]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Tang, Tao |
| 作者单位 | 1.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Tang, Tao,Zhou, Tao. Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2010,8(1):226-248. |
| APA | Tang, Tao,&Zhou, Tao.(2010).Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,8(1),226-248. |
| MLA | Tang, Tao,et al."Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 8.1(2010):226-248. |
入库方式： OAI收割
来源：数学与系统科学研究院
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