Excel In Complex Variables With The Complex Variable Boundary Element Method
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Excel in Complex Variables with the Complex Variable Boundary Element Method
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.
Boundary Elements and other Mesh Reduction Methods XLV
Advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences are reported in the papers that form this volume. As design, analysis and manufacture become more integrated, the chances are that software users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily within the aforementioned integrated process. The maturity of BEM since 1978 has resulted in a substantial number of industrial applications of the method; this demonstrates its accuracy, robustness and ease of use. The range of applications still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. The included papers originate from the 45th conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM) and describe theoretical developments and new formulations, helping to expand the range of applications as well as the type of modelled materials in response to the requirements of contemporary industrial and professional environments.
Boundary Elements and other Mesh Reduction Methods XLIV
The maturity of BEM over the last few decades has resulted in a substantial number of industrial applications of the method; this demonstrates its accuracy, robustness and ease of use. The range of applications still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. Theoretical developments and new formulations have been reported over the last few decades, helping to expand the range of boundary elements and other mesh reduction methods (BEM/MRM) applications as well as the type of modelled materials in response to the requirements of contemporary industrial and professional environments. As design, analysis and manufacture become more integrated, the chances are that software users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily within the aforementioned integrated process. The papers included were presented at the 44th International Conference on Boundary Elements and other Mesh Reduction Methods and report advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences.