Boundary Element Methods

This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems  in $\mathbb{R}^3$. The book is self-contained, the prerequisites on elliptic partial differential and integral equations being presented in Chapters 2 and 3. The main focus is on the development, analysis, and implementation of Galerkin boundary element methods, which is one of the most flexible and robust numerical discretization methods for integral equations. For the efficient realization of the Galerkin BEM, it is essential to replace time-consuming steps in the numerical solution process with fast algorithms. In Chapters 5-9 these methods are developed, analyzed, and formulated in an algorithmic way.

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.