Error analysis for a fast numerical method to a boundary integral equation of the first kind

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	Error analysis for a fast numerical method to a boundary integral equation of the first kind
	Ma, Jingtang 1; Tang, Tao 2
	2008
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	26 期号:1 页码:56-68
摘要	For two-dimensional boundary integral equations of the first kind with logarithmic kernels, the use of the conventional boundary element methods gives linear systems with dense matrix. In a recent work [J. Comput. Math., 22 (2004), pp. 287-298], it is demonstrated that the dense matrix can be replaced by a sparse one if appropriate graded meshes are used in the quadrature rules. The numerical experiments also indicate that the proposed numerical methods require less computational time than the conventional ones while the formal rate of convergence can be preserved. The purpose of this work is to establish a stability and convergence theory for this fast numerical method. The stability analysis depends on a decomposition of the coefficient matrix for the collocation equation. The formal orders of convergence observed in the numerical experiments are proved rigorously.
关键词	boundary integral equation collocation method graded mesh
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000252968400004
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6672
专题	中国科学院数学与系统科学研究院
通讯作者	Ma, Jingtang
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, Beijing 100080, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Ma, Jingtang,Tang, Tao. Error analysis for a fast numerical method to a boundary integral equation of the first kind[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2008,26(1):56-68.
APA	Ma, Jingtang,&Tang, Tao.(2008).Error analysis for a fast numerical method to a boundary integral equation of the first kind.JOURNAL OF COMPUTATIONAL MATHEMATICS,26(1),56-68.
MLA	Ma, Jingtang,et al."Error analysis for a fast numerical method to a boundary integral equation of the first kind".JOURNAL OF COMPUTATIONAL MATHEMATICS 26.1(2008):56-68.