Mathematical and Analytical Techniques with Applications to Engineering

The Fast Solution of Boundary Integral Equations

Authors: Rjasanow, Sergej, Steinbach, Olaf

  • Provides exact descriptions of various mathematical formulations of boundary integral equations in a unified and compact form
  • A systematic numerical treatment of a variety of boundary value problems including the Laplace and Helmholtz equations, and the system of linear elastostatics
  • Numerous examples representing standard problems are given
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eBook $119.00
price for USA in USD (gross)
  • ISBN 978-0-387-34042-5
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Hardcover $159.99
price for USA in USD
  • ISBN 978-0-387-34041-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • ISBN 978-1-4419-4160-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The use of surface potentials to describe solutions of partial differential equations goes back to the middle of the 19th century. Numerical approximation procedures, known today as Boundary Element Methods (BEM), have been developed in the physics and engineering community since the 1950s. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations.

The Fast Solution of Boundary Integral Equations provides a detailed description of fast boundary element methods which are based on rigorous mathematical analysis. In particular, a symmetric formulation of boundary integral equations is used, Galerkin discretisation is discussed, and the necessary related stability and error estimates are derived. For the practical use of boundary integral methods, efficient algorithms together with their implementation are needed. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given which underline both theoretical results and the practical relevance of boundary element methods in typical computations.

The most prominent example is the potential equation (Laplace equation), which is used to model physical phenomena in electromagnetism, gravitation theory, and in perfect fluids. A further application leading to the Laplace equation is the model of steady state heat flow. One of the most popular applications of the BEM is the system of linear elastostatics, which can be considered in both bounded and unbounded domains. A simple model for a fluid flow, the Stokes system, can also be solved by the use of the BEM. The most important examples for the Helmholtz equation are the acoustic scattering and the sound radiation.

Reviews

From the reviews:

"The theoretical and practical study of boundary element methods (BEM) has attracted a lot of attention in the past decades. The main feature of these methods is that one only requires discretization of the surface rather than of the volume of the body to be analyzed. … The present book is intended not only as a useful introduction to classical boundary element techniques but also to some recent developments concerning fast implementation." (María-Luisa Rapún, Mathematical Reviews, Issue 2008 g)


Table of contents (4 chapters)

  • Boundary Integral Equations

    Pages 1-57

  • Boundary Element Methods

    Pages 59-99

  • Approximation of Boundary Element Matrices

    Pages 101-130

  • Implementation and Numerical Examples

    Pages 131-198

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-0-387-34042-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-0-387-34041-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • ISBN 978-1-4419-4160-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Fast Solution of Boundary Integral Equations
Authors
Series Title
Mathematical and Analytical Techniques with Applications to Engineering
Copyright
2007
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-34042-5
DOI
10.1007/0-387-34042-4
Hardcover ISBN
978-0-387-34041-8
Softcover ISBN
978-1-4419-4160-2
Series ISSN
1559-7458
Edition Number
1
Number of Pages
XII, 284
Number of Illustrations and Tables
97 b/w illustrations
Topics