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Fourier BEM

Generalization of Boundary Element Methods by Fourier Transform

  • Book
  • © 2002

Overview

Authors:
  1. Fabian M. E. Duddeck

    1. Lehrstuhl für Baumechanik, Technische Universität München, München, Germany

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  • Concise and clear derivation of the traditional Galerkin-BEM approach
  • Large range of applications from solid mechanics
  • New generalization of BEM
  • Better theoretical insight
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-7
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  2. Introduction

    • Fabian M. E. Duddeck
    Pages 9-13

  3. Traditional BEM

    • Enrico Betti
    Pages 15-24

  4. Distributional BEM

    • Oliver Heaviside
    Pages 25-34

  5. Fourier BEM

    • Jean Baptiste Joseph Fourier
    Pages 35-44

  6. Heat Conduction

    • Siméon Denis Poisson
    Pages 45-61

  7. Elasticity

    • Claude L. M. H. Navier
    Pages 63-72

  8. Plates

    • Gustav Robert Kirchhoff
    Pages 73-94

  9. Waves

    • Lord Rayleigh
    Pages 95-108

  10. Thermoelasticity

    • J. M. C. Duhamel
    Pages 109-114

  11. Non-linearity

    • R. von Mises
    Pages 115-123

  12. Wavelets

    • Alberto Calderón
    Pages 125-137

  13. Conclusions

    • Fabian M. E. Duddeck
    Pages 139-140

  14. Back Matter

    Pages 141-181
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Keywords

About this book

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. However they still demand an explicit expression of a fundamental solution, which is only known in simple cases. In this respect, 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.

Reviews

"In this reviewer’s opinion, the contents of this book, which gathers in a systematic concise fashion several original results due to its author, represents a major contribution to the developments of BEMs and to the literature on them… an elegant and potentially fruitful combination of mathematics and computational mechanics."

Appl Mech Rev

Authors and Affiliations

  • Lehrstuhl für Baumechanik, Technische Universität München, München, Germany

    Fabian M. E. Duddeck

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