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© 2018

Advanced Boundary Element Methods

Treatment of Boundary Value, Transmission and Contact Problems

Benefits

  • Features fundamental chapters on boundary integral equations and their approximations by boundary elements to enable novice readers to become acquainted with a modern field of numerical analysis

  • Discusses advanced key topics in BEM and presents the necessary tools of mathematical analysis, guiding readers to the forefront of reseach

  • Describes numerous numerical experiments to help BEM practitioners in engineering and science understand modern, efficient and reliable versions of BEM

Book

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 52)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Joachim Gwinner, Ernst Peter Stephan
    Pages 1-7
  3. Joachim Gwinner, Ernst Peter Stephan
    Pages 9-41
  4. Joachim Gwinner, Ernst Peter Stephan
    Pages 43-62
  5. Joachim Gwinner, Ernst Peter Stephan
    Pages 63-93
  6. Joachim Gwinner, Ernst Peter Stephan
    Pages 115-222
  7. Joachim Gwinner, Ernst Peter Stephan
    Pages 223-267
  8. Joachim Gwinner, Ernst Peter Stephan
    Pages 269-294
  9. Joachim Gwinner, Ernst Peter Stephan
    Pages 295-332
  10. Joachim Gwinner, Ernst Peter Stephan
    Pages 333-388
  11. Joachim Gwinner, Ernst Peter Stephan
    Pages 389-449
  12. Joachim Gwinner, Ernst Peter Stephan
    Pages 451-536
  13. Joachim Gwinner, Ernst Peter Stephan
    Pages 537-561
  14. Back Matter
    Pages 563-652

About this book

Introduction

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.

Keywords

boundary integral equations boundary element Galerkin and collocation methods contact problems adaptive boundary elements time-domain boundary elements coupling of finite and boundary elements

Authors and affiliations

  1. 1.Fakultät für Luft- und RaumfahrttechnikUniversität der Bundeswehr MünchenNeubiberg/MünchenGermany
  2. 2.Institut für Angewandte MathematikLeibniz Universität HannoverHannoverGermany

About the authors

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.

Bibliographic information

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)