# Foundations of the Complex Variable Boundary Element Method

• Robert Whitley
Book

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

1. Front Matter
Pages i-xii
Pages 1-20
Pages 21-30
Pages 31-49
Pages 51-59
Pages 61-68
Pages 69-76
8. Back Matter
Pages 77-80

### Introduction

This book explains and examines the theoretical underpinnings of the Complex Variable Boundary Element Method (CVBEM) as applied to higher dimensions, providing the reader with the tools for extending and using the CVBEM in various applications. Relevant mathematics and principles are assembled and the reader is guided through the key topics necessary for an understanding of the development of the CVBEM in both the usual two- as well as three- or higher dimensions. In addition to this, problems are provided that build upon the material presented. The Complex Variable Boundary Element Method (CVBEM) is an approximation method useful for solving problems involving the Laplace equation in two dimensions. It has been shown to be a useful modelling technique for solving two-dimensional problems involving the Laplace or Poisson equations on arbitrary domains. The CVBEM has recently been extended to 3 or higher spatial dimensions, which enables the precision of the CVBEM in solving the Laplace equation to be now available for multiple dimensions. The mathematical underpinnings of the CVBEM, as well as the extension to higher dimensions, involve several areas of applied and pure mathematics including Banach Spaces, Hilbert Spaces, among other topics. This book is intended for applied mathematics graduate students, engineering students or practitioners, developers of industrial applications involving the Laplace or Poisson equations, and developers of computer modelling applications.

### Keywords

Banach Spaces Complex Variable Boundary Element Method (CVBEM) Dirichlet Problem Hilbert Spaces Laplace Equations Multi-dimensional Complex Variables Poisson Equations

#### Authors and affiliations

• 1
• Robert Whitley
• 2
1. 1.United States Military AcademyWest PointUSA
2. 2.University of CaliforniaIrvineUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-05954-9
• Copyright Information The Author(s) 2014
• Publisher Name Springer, Cham
• eBook Packages Engineering
• Print ISBN 978-3-319-05953-2
• Online ISBN 978-3-319-05954-9
• Series Print ISSN 2191-530X
• Series Online ISSN 2191-5318
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