Advances In The Complex Variable Boundary Element Method
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Advances in the Complex Variable Boundary Element Method
Author: Theodore V. Hromadka
language: en
Publisher: Springer Science & Business Media
Release Date: 1998
As well as describing the extremely useful applications of the CVBEM, the authors explain its mathematical background -- vital to understanding the subject as a whole. This is the most comprehensive book on the subject, bringing together ten years of work and can boast the latest news in CVBEM technology. It is thus of particular interest to those concerned with solving technical engineering problems -- while scientists, graduate students, computer programmers and those working in industry will all find the book helpful.
Advances in the Complex Variable Boundary Element Method
Author: Theodore V. Hromadka
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
Since its inception by Hromadka and Guymon in 1983, the Complex Variable Boundary Element Method or CVBEM has been the subject of several theoretical adventures as well as numerous exciting applications. The CVBEM is a numerical application of the Cauchy Integral theorem (well-known to students of complex variables) to two-dimensional potential problems involving the Laplace or Poisson equations. Because the numerical application is analytic, the approximation exactly solves the Laplace equation. This attribute of the CVBEM is a distinct advantage over other numerical techniques that develop only an inexact approximation of the Laplace equation. In this book, several of the advances in CVBEM technology, that have evolved since 1983, are assembled according to primary topics including theoretical developments, applications, and CVBEM modeling error analysis. The book is self-contained on a chapter basis so that the reader can go to the chapter of interest rather than necessarily reading the entire prior material. Most of the applications presented in this book are based on the computer programs listed in the prior CVBEM book published by Springer-Verlag (Hromadka and Lai, 1987) and so are not republished here.
The Complex Variable Boundary Element Method
Author: T. V. Hromadka
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-12
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.