| 边界元方法中的奇异性 |
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| 引用本文： | 祝家麟.边界元方法中的奇异性[J].土木建筑与环境工程,1991,13(2). |
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| 作者姓名： | 祝家麟 |
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| 作者单位： | 重庆建筑工程学院基础科学系 |
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| 摘 要： | 本文试图从数值计算和从数学分析的角度全面地评述现阶段边界元方法研究中对奇异性的处理.列出了计算奇异积分和超奇异积分的方法;讨论了由于边界的非光滑性引起的解的奇异性;介绍了描述它们的数学工具,如在部分边界上定义的索伯列夫空间,拟微分算子等.为将奇异性反映在边界元近似中,建议采用奇异边界单元.
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| 关 键 词： | 边界元法 奇异性 奇异积分 非光滑边界 奇异边界单元 |
SINGULARITIES IN BOUNDARY ELEMENT METHODS |
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| Zhu Jialin.SINGULARITIES IN BOUNDARY ELEMENT METHODS[J].土木建筑与环境工程,1991,13(2). |
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| Authors: | Zhu Jialin |
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| Affiliation: | Zhu Jialin Department of Natural Science |
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| Abstract: | This paper presents an all round review of recent deve-lopments in treating the singularities in boundary element methods bothfor numerical computing and for mathematical analysing.Approachesfor numerical treatment of singular and hyper-singular integrations arelisted.Singular behaviour of solution on non-smooth boundary are discus-sed and the mathematical tools for describing it,such as the Sobolevspaces defined on a part of boundary,the pseudo-differential operatorsare presented.In order to incorporate the singular behaviour into theboundary element approximation,the technique of introducing singularboundary element is suggested. |
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| Keywords: | boundary element method singularity singular integral non-smooth boundary singular boundary element |
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