Review of Dual Boundary Element Methods With Emphasis on Hypersingular Integrals and Divergent Series

[+] Author and Article Information
J. T. Chen

Department of Harbor and River Engineering, Taiwan Ocean University, Keelung, Taiwan

H.-K. Hong

Department of Civil Engineering, Taiwan University, Taipei, Taiwan

Appl. Mech. Rev 52(1), 17-33 (Jan 01, 1999) (17 pages) doi:10.1115/1.3098922 History: Online April 14, 2009


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.

Copyright © 1999 by American Society of Mechanical Engineers
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