The Complex Variable Boundary Element Method

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The Complex Variable Boundary Element Method In Engineering Analysis

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Author : Theodore V. Hromadka
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Complex Variable Boundary Element Method In Engineering Analysis written by Theodore V. Hromadka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Medical categories.

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

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Author : Theodore V. Hromadka
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Advances In The Complex Variable Boundary Element Method written by Theodore V. Hromadka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

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

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Author : T. V. Hromadka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-12

The Complex Variable Boundary Element Method written by T. V. Hromadka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-12 with Mathematics categories.

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.

A Multi Dimensional Complex Variable Boundary Element Method

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Author : Theodore V. Hromadka
language : en
Publisher: Computational Mechanics
Release Date : 2002

A Multi Dimensional Complex Variable Boundary Element Method written by Theodore V. Hromadka and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Boundary element methods categories.

The Complex Variable Boundary Element Method (CVBEM) is a numerical technique useful in developing approximations of boundary value problems involving the LaPlace and Poisson partial differential equations. Because the CVBEM is based upon the Cauchy integral theorem of complex variables, it has so far been limited to two-dimensional geometry applications.

Advances In The Complex Variable Boundary Element Method

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Author : Theodore V. Hromadka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Advances In The Complex Variable Boundary Element Method written by Theodore V. Hromadka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Technology & Engineering categories.

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.

Foundations Of The Complex Variable Boundary Element Method

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Author : Theodore Hromadka
language : en
Publisher:
Release Date : 2014-04-30

Foundations Of The Complex Variable Boundary Element Method written by Theodore Hromadka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-30 with categories.

A Beginner S Course In Boundary Element Methods

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Author : Whye-Teong Ang
language : en
Publisher: Universal-Publishers
Release Date : 2007

A Beginner S Course In Boundary Element Methods written by Whye-Teong Ang and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This is a course in boundary element methods for the absolute beginners. Basic concepts are carefully explained through the use of progressively more complicated boundary value problems in engineering and physical sciences. The readers are assumed to have prior basic knowledge of vector calculus (covering topics such as line, surface and volume integrals and the various integral theorems), ordinary and partial differential equations, complex variables, and computer programming. Electronic ebook edition available at Powells.com. Click on Powells logo to the left.

Boundary Element Methods In Heat Transfer

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Author : Wrobel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Boundary Element Methods In Heat Transfer written by Wrobel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Heat transfer problems in industry are usually of a very complex nature, simultaneously involving different transfer modes such as conduction, convection, radiation and others. Because of this, very few problems can be solved analytically and one generally has to resort to numerical analysis. The boundary element method is a numerical technique which has been receiving growing attention for solving heat transfer problems because of its unique ability to confine the discretization process to the boundaries of the problem region. This allows major reductions in the data preparation and computer effort necessary to solve complex industrial problems. The purpose of this book is to present efficient algorithms used in conjunction with the boundary element method for the solution of steady and transient, linear and non-linear heat transfer problems. It represents the state-of-the-art of boundary element applications in the field of heat transfer, and constitutes essential reading for researchers and practising engineers involved with this important topic.

Excel In Complex Variables With The Complex Variable Boundary Element Method

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Author : B. D. Wilkins
language : en
Publisher: WIT Press
Release Date : 2021-09-22

Excel In Complex Variables With The Complex Variable Boundary Element Method written by B. D. Wilkins and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-22 with Mathematics categories.

Using the familiar software Microsoft ® Excel, this book examines the applications of complex variables. Implementation of the included problems in Excel eliminates the “black box” nature of more advanced computer software and programming languages and therefore the reader has the chance to become more familiar with the underlying mathematics of the complex variable problems. This book consists of two parts. In Part I, several topics are covered that one would expect to find in an introductory text on complex variables. These topics include an overview of complex numbers, functions of a complex variable, and the Cauchy integral formula. In particular, attention is given to the study of analytic complex variable functions. This attention is warranted because of the property that the real and imaginary parts of an analytic complex variable function can be used to solve the Laplace partial differential equation (PDE). Laplace's equation is ubiquitous throughout science and engineering as it can be used to model the steady-state conditions of several important transport processes including heat transfer, soil-water flow, electrostatics, and ideal fluid flow, among others. In Part II, a specialty application of complex variables known as the Complex Variable Boundary Element Method (CVBEM) is examined. CVBEM is a numerical method used for solving boundary value problems governed by Laplace's equation. This part contains a detailed description of the CVBEM and a guide through each step of constructing two CVBEM programs in Excel. The writing of these programs is the culminating event of the book. Students of complex variables and anyone with an interest in a novel method for approximating potential functions using the principles of complex variables are the intended audience for this book. The Microsoft Excel applications (including simple programs as well as the CVBEM program) covered will also be of interest in the industry, as these programs are accessible to anybody with Microsoft Office.

Computational Aspects

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Author : Carlos A. Brebbia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-12

Computational Aspects written by Carlos A. Brebbia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-12 with Science categories.

Past volumes of this series have concentrated on the theoretical and the more formal aspects of the boundary element method. The present book instead stresses the computational aspects of the technique and its applications with the objective of facilitating the implementation of BEM in the engineering industry and its better understanding in the teaching and research environments. The book starts by discussing the topics of convergence of solutions, application to nonlinear problems and numerical integration. This is followed by a long chapter on the computational aspects of the method, discussing the different numerical schemes and the way in which influence functions can be computed. Three separate chapters deal with important techniques which are related to classical boundary elements, namely the edge method, multigrid schemes and the complex variable boundary element approach. The last two chapters are of special interest as they present and explain in detail two FORTRAN codes which have numerous applications in engineering, i.e. a code for the solution of potential problems and another for elastostatics. Each sub routine in the programs is listed and explained. The codes follow the same format as the ones in the classical book "The Boundary Element Method for Engineers" (by C. A. Brebbia, Computational Mechanics Publications, first published in 1978) but are more advanced in terms of elements and capabilities. In particular the new listings deal with symmetry, linear elements for the two dimensional elasticity, some mixed type of boundary conditions and the treatment of infinite regions.