George C. Hsiao, Wolfgang L. Wendland

Boundary Integral Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book is devoted to the basic mathematical properties of solutions to boundary integral equations and presents a systematic approach to the variational methods for the boundary integral equations arising in elasticity, fluid mechanics, and acoustic scattering theory. It may also serve as the mathematical foundation of the boundary element methods. The latter have recently become extremely popular and efficient computational tools in applications. The authors are well known for their fundamental work on boundary integral equations and related topics. This book is a major scholarly contribution to the modern theory of boundary integral equations and should be accessible and useful to a large community of mathematical analysts, applied mathematicians, engineers and scientists.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 620
• Erscheinungstermin: 7. Mai 2008
• Englisch
• ISBN-13: 9783540685456
• Artikelnr.: 37369481

Autorenporträt

George C. Hsiao received a bachelor's degree in Civil Engineering from  National Taiwan University, a master's degree from Carnegie Institute of Technology in the same field,  and a doctorate degree in Mathematics  from Carnegie Mellon University. He is now the Carl J. Rees Professor of Mathematics Emeritus at the University of Delaware from which he retired in September 2012 after 43 years on the faculty of the Department of Mathematical Sciences. His primary research interests are integral equations and partial differential equations with their applications in mathematical physics and continuum mechanics. Wolfgang L. Wendland, now Professor Emeritus at the University Stuttgart was studying mechanical engineering and mathematics at the Technical University Berlin and became Full Professor for Mathematics 1970-1986 at the TU Darmstadt and 1986-2005 at the University Stuttgart. His research interests are in Applied Mathematics with emphasis on partial differential equations and integral equations as well as approximation and numerical methods with applications to continuum mechanics of flow and elasticity problems. Both authors are well known for their fundamental work on boundary integral equations and related topics.

Inhaltsangabe

Boundary Integral Equations.- Representation Formulae, Local Coordinates and Direct Boundary Integral Equations.- Sobolev Spaces.- Variational Formulations.- to Pseudodifferential Operators.- Pseudodifferential Operators as Integral Operators.- Pseudodifferential and Boundary Integral Operators.- Integral Equations on ?? IR3 Recast as Pseudodifferential Equations.- Boundary Integral Equations on Curves in IR2.

Rezensionen

From the reviews:

"The main goal of this book is to explain the mathematical foundation of the boundary element methods (BEMs) ... . The BEM is well developed and widely used by engineers and scientists in applied mathematical computations for 40 years. ... The book will be helpful not only for mathematicians who want to become familiar with the BIE but also for users of BEMs who want to understand mathematical background of the computational method." (Vladimir Sládek, Zentralblatt MATH, Vol. 1157, 2009)

"This book has been in preparation for many years: the care in its composition is evident. ... The development of ... analytical framework occupies the major part of this impressive book. ... There are 10 chapters and a bibliography of 325 items. ... In summary, this is an important scholarly work on the modern mathematical theory of boundary integral equations." (Paul Andrew Martin, Mathematical Reviews, Issue 2009 i)