A Computational Mechanics Publication
Preface
The Complex Variable Boundary Element Method or CVBEM provides a mathematical modeling technique for approximating boundary value problems of the Laplace equation in two-dimensions. That is, potential problems involving steady state heat flow, soil water flow, electrostatics, stress-strain torsion effects, and many other problems can be numerically solved using the CVBEM.
In this book are presented the basics of the CVBEM and the recent advances of the CVBEM into the classic L 2 theory of best approximations. Sufficient detail and mathematic rigor is presented to enable the reader to comprehend the numerical technique without extensive prerequisite study. Computer software listings in FORTRAN are included for 5 CVBEM programs (CVBEML through CVBEM5) along with several example problems to demonstrate the use of the several CVBEM numerical techniques in engineering and scientific studies of potential problems. Finally, the general purpose CVBEM1 program is provided on the included floppy disc for use with IBM compatible microcomputers.
Contents
I. Complex Variable Boundary Elements Background And Development
I.0Introduction
I.1 A Complex Variable Boundary Element Approximation Model
I.2 The Analytic Function Defined By The Approximation w (Z)
I.3 A Constant Boundary Element Method
I.4 The Complex Variable Boundary Element Method
I.5 Approximation Error From The CVBEM
I.6 A CVBEM Modeling Strategy To Reduce Approximation Error
I.7 Expansion Of The H, Approximation Function
I.8 Upper Half Plane Boundary Value Problems
I.9 The Approximate Boundary For Error Analysis
I.10 Locating Additional Nodal Points On _
I.11 Sources And Sinks
I.12 Regional Inhomogeneity
I.13 The Poisson Equation
I.14 Computer-Aided-Analysis And The CVBEM
References
Ii. Complex Variable Boundary Element (CVBE) Basics
Ii.0 Introduction
Ii.1 Nodal Points
Ii.2 CVBE
Ii.3 Boundary Conditions
Ii.4 Symmetry
Ii.5 Sources And Sinks
Ii.6 Dissimilar Materials
Ill. CVBEM1 Program
111.0 Introduction
111.1 Capabilities of the CVBEM1 Program
111.2 Program Listing
111.3 User's Instructions
IV. CVBEM1 Program Applications
V. CVBEM2 Program
V.0 Introduction
V.1 Capability Of Cvbem2 Program
V.2 Program Listing
V.3 User's Instructions
VI. Cvbem2 Program Applications
VII. Cvbem3 Program
VII.0 Introduction
VII.1 Capability Of Cvbem3 Program
VII.2 Program Listing
VII.3 User's Instructions
VIII. CVBEM3 Program Applications
IX. The CVBEM And E2 Spaces
IX.0 Introduction
IX.1 Basic Theory Of E2( _) Spaces
IX.2 Elements Of Conformal Mapping
IX.3 Almost Everywhere (ae) Equivalence
IX.4 Development Of A Norm And Inner-Product On W_
IX.5 Global Trial Function Development And The CVBEM
IX.6 The CVBEM Approximation Function
IX.7 Approximation In Measure
IX.8 CVBEM Approximations In The Least Square Sense
References
X. CVBEM4 Program
X.0 Introduction
X.1 Capabilitiesofcvbem4program
X.2 Program Listing
X.3 User's Instructions
XI. CVBEM4 Program Applications
References
XII. CVBEM5 Program
XII.0 Introduction
