Overview
- Provides an exact mathematical description of various mathematical formulations and numerical methods for boundary integral equations in the three-dimensional case in a unified and compact form
- a systematic numerical treatment of a variety of boundary value problems for the Laplace equation, for the system of linear elastostatics, and for the Helmholtz equation.
- Numerous examples representing standard problems are given which underline both theoretical results and the practical relevance of boundary element methods in typical computations
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical and Analytical Techniques with Applications to Engineering (MATE)
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Table of contents (4 chapters)
Keywords
About this book
Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences. 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 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.
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.
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)
Authors and Affiliations
Bibliographic Information
Book Title: The Fast Solution of Boundary Integral Equations
Authors: Sergej Rjasanow, Olaf Steinbach
Series Title: Mathematical and Analytical Techniques with Applications to Engineering
DOI: https://doi.org/10.1007/0-387-34042-4
Publisher: Springer New York, NY
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag US 2007
Hardcover ISBN: 978-0-387-34041-8Published: 15 May 2007
Softcover ISBN: 978-1-4419-4160-2Published: 19 November 2010
eBook ISBN: 978-0-387-34042-5Published: 17 April 2007
Series ISSN: 1559-7458
Series E-ISSN: 1559-7466
Edition Number: 1
Number of Pages: XII, 284
Number of Illustrations: 97 b/w illustrations
Topics: Mathematics, general, Mathematical and Computational Engineering, Applications of Mathematics, Theoretical, Mathematical and Computational Physics, Image Processing and Computer Vision, Ordinary Differential Equations