Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods

This book is devoted to a thorough treatment of preconditioners for boundary element discretisations of first-kind integral equations. The book focusses on domain-decomposition-type methods and multilevel methods. The reader will gain good understanding of the mechanism and necessary techniques in the analysis of the preconditioners. These techniques are unique for the discretisation of first-kind integral equations because the resulting systems of linear equations are not only large and ill-conditioned but also dense.

The book showcases state-of-the-art preconditioning techniques for boundary integral equations with up-to-date research. A thorough treatment of Sobolev spaces of fractional orders familiarises the reader with important mathematical tools for the analysis. The concise presentation of adaptive BEM, hp-version BEM, and coupling of FEM-BEM provides the reader with very efficient computational tools for solving practical problems with applications in science and engineering.

Publication Year: 2021
Imprint: Springer International Publishing