Applied Mathematical Sciences: Boundary Integral Equations

George C. Hsiao · Wolfgang L. Wendland

Mar 2021 · Applied Mathematical Sciences Edisi #164 · Springer Nature

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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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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.

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