Gwinner J., Stephan E.P. Advanced Boundary Element Methods: Treatment of Boundary Value, Transmission and Contact Problems

Springer, 2018. — 661 p. — (Springer Series in Computational Mathematics 52). — ISBN: 3319920006.This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods – efficient computational tools that have become extremely popular in applications.
Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research.Some Elements of Potential Theory
A Fourier Series Approach
Mixed BVPs, Transmission Problems and Pseudodifferential Operators
The Signorini Problem and More Nonsmooth BVPs and Their Boundary Integral Formulation
A Primer to Boundary Element Methods
Advanced BEM for BVPs in Polygonal/Polyhedral Domains: h- and p-Versions
Exponential Convergence of hp-BEM
Mapping Properties of Integral Operators on Polygons
A-BEM
BEM for Contact Problems
FEM-BEM Coupling
Time-Domain BEM