ISBN-10:
3642057330
ISBN-13:
9783642057335
Pub. Date:
12/08/2010
Publisher:
Springer Berlin Heidelberg
Boundary Integral Equations / Edition 1

Boundary Integral Equations / Edition 1

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Overview

Boundary Integral Equations / Edition 1

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.

Product Details

ISBN-13: 9783642057335
Publisher: Springer Berlin Heidelberg
Publication date: 12/08/2010
Series: Applied Mathematical Sciences , #164
Edition description: Softcover reprint of hardcover 1st ed. 2008
Pages: 620
Product dimensions: 6.10(w) x 9.25(h) x 0.05(d)

Table of Contents

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.

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