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Fourier BEM

Generalization of Boundary Element Methods by Fourier Transform

  • Fabian M. E. Duddeck

Part of the Lecture Notes in Applied Mechanics book series (LNACM, volume 5)

Table of contents

  1. Front Matter
    Pages i-7
  2. Fabian M. E. Duddeck
    Pages 9-13
  3. Enrico Betti
    Pages 15-24
  4. Oliver Heaviside
    Pages 25-34
  5. Jean Baptiste Joseph Fourier
    Pages 35-44
  6. Siméon Denis Poisson
    Pages 45-61
  7. Claude L. M. H. Navier
    Pages 63-72
  8. Gustav Robert Kirchhoff
    Pages 73-94
  9. Lord Rayleigh
    Pages 95-108
  10. J. M. C. Duhamel
    Pages 109-114
  11. R. von Mises
    Pages 115-123
  12. Alberto Calderón
    Pages 125-137
  13. Fabian M. E. Duddeck
    Pages 139-140
  14. Back Matter
    Pages 141-181

About this book

Introduction

Like FEM, the boundary element method (BEM) provides a general numerical tool for the solution of complex engineering problems. In the last decades, the range of its applications has remarkably been enlarged. Therefore dynamic and nonlinear problems can be tackled. Nevertheless, they still demand an explicit expression of a fundamental solution, which is only known in simple cases. Therefore, the present book proposes an alternative BEM-formulation based on the Fourier transform, which can be applied to almost all cases relevant in engineering mechanics. The basic principle is presented for the heat equation. Applications are taken from solid mechanics (e.g. poroelasticity, thermoelasticity). Transient and stationary examples are given as well as linear and nonlinear. Completed with a mathematical and mechanical glossary, the book will serve as a comprehensive text book linking applied mathematics to real world engineering problems.

Keywords

Fourier transform Numerical integration Singular integral Wavelet engineering mechanics finite element method linearity

Authors and affiliations

  • Fabian M. E. Duddeck
    • 1
  1. 1.Lehrstuhl für BaumechanikTechnische Universität MünchenMünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-45626-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07727-2
  • Online ISBN 978-3-540-45626-1
  • Series Print ISSN 1613-7736
  • Series Online ISSN 1860-0816
  • Buy this book on publisher's site