Overview

This book is devoted to the mathematical foundation of boundary integral equations. The combination of ?nite element analysis on the boundary with these equations has led to very e?cient computational tools, the boundary element methods (see e.g., the authors [139] and Schanz and Steinbach (eds.) [267]). Although we do not deal with the boundary element discretizations in this book, the material presented here gives the mathematical foundation of these methods. In order to avoid over generalization we have con?ned ourselves to the treatment of elliptic boundary value problems. The central idea of eliminating the ?eld equations in the domain and - ducing boundary value problems to equivalent equations only on the bou- ary requires the knowledge of corresponding fundamental solutions, and this idea has a long history dating back to the work of Green [107] and Gauss [95, 96]. Today the resulting boundary integral equations still serve as a major tool for the analysis and construction of solutions to boundary value problems.

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9783540152842

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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 Sladek, 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)

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