# The Complex Variable Boundary Element Method

Book

Part of the Lecture Notes in Engineering book series (LNENG, volume 9)

1. Front Matter
Pages N2-XI
Pages 1-10
Pages 11-45
Pages 46-100
Pages 101-161
Pages 162-204
Pages 205-241
8. Back Matter
Pages 242-245

### Introduction

The Complex Variable Boundary Element Method or CVBEM is a generalization of the Cauchy integral formula into a boundary integral equation method or BIEM. This generalization allows an immediate and extremely valuable transfer of the modeling techniques used in real variable boundary integral equation methods (or boundary element methods) to the CVBEM. Consequently, modeling techniques for dissimilar materials, anisotropic materials, and time advancement, can be directly applied without modification to the CVBEM. An extremely useful feature offered by the CVBEM is that the pro­ duced approximation functions are analytic within the domain enclosed by the problem boundary and, therefore, exactly satisfy the two-dimensional Laplace equation throughout the problem domain. Another feature of the CVBEM is the integrations of the boundary integrals along each boundary element are solved exactly without the need for numerical integration. Additionally, the error analysis of the CVBEM approximation functions is workable by the easy-to-understand concept of relative error. A sophistication of the relative error analysis is the generation of an approximative boundary upon which the CVBEM approximation function exactly solves the boundary conditions of the boundary value problem' (of the Laplace equation), and the goodness of approximation is easily seen as a closeness-of-fit between the approximative and true problem boundaries.

### Keywords

Boundary Fluid Numerical integration Taylor series boundary element method complex number constant form integral integral equation model modeling potential theory theorem variable

#### Authors and affiliations

• 1
1. 1.Department of Civil EngineeringUniversity of CaliforniaIrvineUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-82361-9
• Copyright Information Springer-Verlag Berlin Heidelberg 1984
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-13743-6
• Online ISBN 978-3-642-82361-9
• Series Print ISSN 0176-5035
• Buy this book on publisher's site
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