This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.

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"The theoretical and practical study of boundary element methods (BEM) has attracted a lot of attention in the past decades. The main feature of these methods is that one only requires discretization of the surface rather than of the volume of the body to be analyzed. ... The present book is intended not only as a useful introduction to classical boundary element techniques but also to some recent developments concerning fast implementation." (Mar�a-Luisa Rap�n, Mathematical Reviews, Issue 2008 g)

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