The Complex Variable Boundary Element Method
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The Complex Variable Boundary Element Method in Engineering Analysis
Author: Theodore V. Hromadka
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The Complex Variable Boundary Element Method (CVBEM) has emerged as a new and effective modeling method in the field of computational mechanics and hydraulics. The CVBEM is a generalization of the Cauchy integral formula into a boundary integral equation method. The model ing approach by boundary integration, the use of complex variables for two-dimensional potential problems, and the adaptability to now-popular microcomputers are among the factors that make this technique easy to learn, simple to operate, practical for modeling, and efficient in simulating various physical processes. Many of the CVBEM concepts and notions may be derived from the Analytic Function Method (AFM) presented in van der Veer (1978). The AFM served as the starting point for the generalization of the CVBEM theory which was developed during the first author's research engagement (1979 through 1981) at the University of California, Irvine. The growth and expansion of the CVBEM were subsequently nurtured at the U. S. Geological Survey, where keen interest and much activity in numerical modeling and computational mechanics-and-hydraulics are prevalent. Inclusion of the CVBEM research program in Survey's computational-hydraulics projects, brings the modeling researcher more uniform aspects of numerical mathematics in engineering and scientific problems, not to mention its (CVBEM) practicality and usefulness in the hydrologic investigations. This book is intended to introduce the CVBEM to engineers and scientists with its basic theory, underlying mathematics, computer algorithm, error analysis schemes, model adjustment procedures, and application examples.
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.
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.