Advanced Boundary Element Methods: Treatment of Boundary Value, Transmission and Contact Problems

by Joachim Gwinner, Ernst Peter Stephan

Overview

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.

The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

Product Details

ISBN-13:	9783319920009
Publisher:	Springer International Publishing
Publication date:	07/29/2018
Series:	Springer Series in Computational Mathematics , #52
Edition description:	1st ed. 2018
Pages:	652
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Joachim Gwinner is retired professor of mathematics at Bundeswehr University Munich. His research interests span from optimization to numerical and variational analysis with applications in continuum mechanics.

Ernst Peter Stephan is retired professor of mathematics at Leibniz University Hannover. His research covers numerical methods for partial differential equations and boundary integral equations together with their analysis.

Table of Contents

1 Introduction.- 2 Some Elements of Potential Theory.- 3 A Fourier Series Approach.- 4 Mixed BVPs, Transmission Problems and Pseudodifferential Operators.- 5 The Signorini Problem and More Nonsmooth BVPs and Their Boundary Integral Formulation.- 6 A Primer to Boundary Element Methods.- 7 Advanced BEM for BVPs in Polygonal/Polyhedral Domains: h- and p-Versions.- 8 Exponential Convergence of hp-BEM.- 9 Mapping Properties of Integral Operators on Polygons.- 10 A-BEM.- 11 BEM for Contact Problems.- 12 FEM-BEM Coupling.- 13 Time-Domain BEM.- A Linear Operator Theory.- B Pseudodifferential Operators.- C Convex and Nonsmooth Analysis, Variational Inequalities.- D Some Implementation for BEM.- References.- Index.

Editorial Reviews

The book can be recommended to researches in the field of mathematics and engineering and to graduate students to familiarize themselves with the state-of-the-art of boundary element methods.” (Dana Černá, zbMATH 1429.65001, 2020)

“The book can be recommended as a comprehensive set of results for the state of the art in BEM, and in the applications considered by the authors.” (Michael J. Carley, Mathematical Reviews, August, 2019)

From the Publisher