Review of Dual Boundary Element Methods With Emphasis on Hypersingular Integrals and Divergent Series
Review of Dual Boundary Element Methods With Emphasis on Hypersingular Integrals and Divergent Series
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DOI：
10.1115/1.3098922
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发表时间：
1999
影响因子：
14.3
通讯作者：
Jeng-Tzong Chen;H. Hong
中科院分区：
文献类型：
--
作者：
Jeng-Tzong Chen;H. Hong
本文介绍了对偶边界元方法的发展现状，重点介绍了超奇异积分和发散级数的正则化。通过一个简单的例子，给出了间断函数及其导数的对偶积分表示和对偶级数表示，从而说明了对偶边界元法中的正则化问题。超奇异性和发散级数理论的双重表示的框架下，他们的关系和正则化技术进行审查。探讨了超奇异性和发散级数对偶边界元法的应用。这篇评论文章包含249篇参考文献。
This article provides a perspective on the current status of the formulations of dual boundary element methods with emphasis on the regularizations of hypersingular integrals and divergent series. A simple example is given to show the dual integral representation and the dual series representation for a discontinuous function and its derivative and thereby to illustrate the regularization problems encountered in dual boundary element methods. Hypersingularity and the theory of divergent series are put under the framework of the dual representations, their relation and regularization techniques being examined. Applications of the dual boundary element methods using hypersingularity and divergent series are explored. This review article contains 249 references.