This volume contains eleven state of the art contributions on boundary integral equation and boundary element methods. Beside some historical and more analytical aspects in the formulation and analysis of boundary integral equations also modern fast boundary element methods are described and analyzed from a mathematical point of view. In addition, engineering and industrial applications of those methods are presented showing the ability of state of the art boundary element methods to solve challenging problems from different fields of applications.

This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in industry.

Some Historical Remarks on the Positivity of Boundary Integral Operators.- Averaging Techniques for a Posteriori Error Control in Finite Element and Boundary Element Analysis.- Coupled Finite and Boundary Element Domain Decomposition Methods.- The hp-Version of the Boundary Element Method for the Lamé Equation in 3D.- Sparse Convolution Quadrature for Time Domain Boundary Integral Formulations of the Wave Equation by Cutoff and Panel-Clustering.- Fast Multipole Methods and Applications.- A Fast Boundary Integral Equation Method for Elastodynamics in Time Domain and Its Parallelisation.- FM-BEM and Topological Derivative Applied to Acoustic Inverse Scattering.- Boundary Element Methods for Eddy Current Computation.- Fast Boundary Element Methods in Computational Electromagnetism.- BEM-Based Simulations in Engineering Design.