Boundary Element Methods

- Preface

- Introduction

- Elliptic Differential Equations

- Elliptic Boundary Integral Equations

- Boundary Element Methods

- Generating the Matrix Coefficients

- Solution of Linear Systems of Equations

- Cluster Methods

- Parametric Surface Approximation

- A Posteriori Error Estimation

- Bibliography

- Index of Symbols

- Index

Prof. Dr. rer. nat. Stefan Sauter Born in 1964, Heidelberg, Germany. Studies of mathematics and physics at the University of Heidelberg (1985-1990). Scientific assistant at the University of Kiel (PhD 1993). 1993/94 PostDoc at the University of College Park. Until 1998, senior assistant at the University of Kiel (Habilitation 1998). Chair in Mathematics at the University of Leipzig (1998/99). Since 1999 Ordinarius in Mathematics at the Universität Zürich.

Prof. Christoph Schwab, PhD Born in 1962, Flörsheim, Germany. Studies of mathematics, mechanics, and aerospace engineering in Darmstadt and College Park, Maryland, USA (1982-1989). PhD in Applied Mathematics, University of Maryland, College Park 1989. Postdoctoral fellow (1990/91) University of Westminster, London, UK. Assistant professor (1991-1994) and associate professor (1995) of Mathematics, University of Maryland, Baltimore County, USA. Extraordinarius (1995-1998) and Ordinarius (1998-) for mathematics at the ETH Zürich.

The authors were organizing various conferences and minisymposia on fast boundary element methods, e.g., at Oberwolfach, MAFELAP conferences at Brunel UK, Zurich Summer Schools, and were speakers on these topics at numerous international conferences.

From the reviews:

"The book's main focus 'is the systematic development of numerical methods to determine the Galerkin solution of boundary integral equations' (BIEs) in the context of three-dimensional elliptic boundary value problems (BVPs). ... There are separate studies of transmission problems, screen problems, and exterior BVPs for the Helmholtz equation. ... In summary, this is a well-written book on the numerical analysis of Galerkin methods for the solution of boundary integral equations." (Paul Andrew Martin, Mathematical Reviews, Issue 2011 i)

"This book is ... the most comprehensive and self-contained book on BEMs of the ones that exist ... . The book is written rigorously and is an important scholarly contribution to the area of boundary elements. ... this book is an excellent mathematical monograph and valuable reference not only for researchers in the field of BEMs but also for applied mathematicians, engineers, and scientists who are interested in modern computational mathematics. The authors have produced a commendable work of scholarly achievement." (George C. Hsiao, SIAM Review, Vol. 54 (1), March, 2012)

"The focus of the book is the systematic development of numerical methods to determine the Galerkin approximate solution of boundary integral equations ... . The core of the book can be used as the basis for a lecture course on the numerics of boundary integral equation or as an introduction for non-specialists to the development, analysis and implementation of efficient BE methods. Complementary material bridges the gap between a textbook and current research areas, which makes the book useful also for specialists in BEM." (Gunther Schmidt, Zentralblatt MATH, Vol. 1215, 2011)

From the reviews:

"The book's main focus 'is the systematic development of numerical methods to determine the Galerkin solution of boundary integral equations' (BIEs) in the context of three-dimensional elliptic boundary value problems (BVPs). ... There are separate studies of transmission problems, screen problems, and exterior BVPs for the Helmholtz equation. ... In summary, this is a well-written book on the numerical analysis of Galerkin methods for the solution of boundary integral equations." (Paul Andrew Martin, Mathematical Reviews, Issue 2011 i)

"This book is ... the most comprehensive and self-contained book on BEMs of the ones that exist ... . The book is written rigorously and is an important scholarly contribution to the area of boundary elements. ... this book is an excellent mathematical monograph and valuable reference not only for researchers in the field of BEMs but also for applied mathematicians, engineers, and scientists who are interested in modern computational mathematics. The authors have produced a commendable work of scholarly achievement." (George C. Hsiao, SIAM Review, Vol. 54 (1), March, 2012)

"The focus of the book is the systematic development of numerical methods to determine the Galerkin approximate solution of boundary integral equations ... . The core of the book can be used as the basis for a lecture course on the numerics of boundary integral equation or as an introduction for non-specialists to the development, analysis and implementation of efficient BE methods. Complementary material bridges the gap between a textbook and current research areas, which makes the book useful also for specialists in BEM." (Gunther Schmidt, Zentralblatt MATH, Vol. 1215, 2011)