Singular Integrals in Boundary Element Methods (Advances in Boundary Elements Vol 3) - Hardcover

Vladimir Sladek

Hardcover

ISBN 10: 1853125334 ISBN 13: 9781853125331

Publisher: WIT Press / Computational Mechanics, 1998

Synopsis

This book provides a comprehensive treatment of singular integrals in Boundary Element Methods, including both theoretical and numerical treatment. The authors document the efficiency of various techniques with numerical experiments.

Boundary Element Methods use singular solutions (fundamental solutions of the governing equations) in contrast to other discretization methods such as finite element or finite difference methods. The presence of the mathematical singularity in otherwise (physically) non-singular problems gives rise to the need for accurate computation of singular integrals. This requirement has attracted the attention of BEM researchers from the very beginning.

Sometimes the appearance of singular integrals in BEM formulations has been thought to be a handicap in computation, which is compensated for by the dimensional reduction of the problems. In fact, singular integrals should be recognized as a source of effectiveness and stability in the numerical solution, if these integrals are properly treated. The overall accuracy of BEM solutions is largely dependent on the precision with which various integrals are evaluated. No doubt, the evaluation of singular integrals requires much more sensitive treatment than that of regular integrals. Therefore, a proper consideration and evaluation of singular integrals is one of the most frequently discussed topics in boundary element research.

This book gives the state-of-the-art of theoretical and numerical treatment of singular integrals in BEM's. Both the boundary and domain integrals are considered in tow- and there-dimensional boundary value problems as well a the use of symbolic computation and the formulation using complex arithmetic in the case of plane problems are outlined. From the physical point of view, the formulations concern the potential problems, elasticity, plate and crack problems. The present techniques have a universal character and can be easily applied to solution of a variety of engineering problems. The book can be found to be useful not only for understanding the nature and treatment of singular integrals in BEM's, but also in motivation for further research in this field. Therefore, it is recommended for graduate students, and researchers as well as for the users of boundary element methods in various computational applications.

About this title

From the Author

No other recent published book provides such comprehensive coverage of the topic.

Review

..".a good source of information for experienced researchers investigating advanced BIE formulations...and for learning the main issues associated with its further development." --AIAA JOURNAL, Vol 38, No4, April 2000

Edition details

• Publisher: WIT Press / Computational Mechanics
• Publication date: 1998
• Language: English
• ISBN 10: 1853125334
• ISBN 13: 9781853125331
• Binding: Hardcover
• Number of pages: 448
• Editor: Vladimir Sladek, J. Sladek