chapter 15 - Chapter 15 NUMERICAL METHODS The recipe for...

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Chapter 15 NUMERICAL METHODS The recipe for ignorance is: be satisfied with your opinions and content with your knowledge. —ELBERT HUBBARD 15.1 INTRODUCTION In the preceding chapters we considered various analytic techniques for solving EM prob- lems and obtaining solutions in closed form. A closed form solution is one in the form of an explicit, algebraic equation in which values of the problem parameters can be substituted. Some of these analytic solutions were obtained assuming certain situations, thereby making the solutions applicable to those idealized situations. For example, in deriving the formula for calculating the capacitance of a parallel-plate capacitor, we assumed that the fringing effect was negligible and that the separation distance was very small compared with the width and length of the plates. Also, our application of Laplace's equation in Chapter 6 was restricted to problems with boundaries coinciding with coordinate surfaces. Analytic solutions have an inherent advantage of being exact. They also make it easy to observe the behavior of the solution for variation in the problem parameters. However, an- alytic solutions are available only for problems with simple configurations. When the complexities of theoretical formulas make analytic solution intractable, we resort to nonanalytic methods, which include (1) graphical methods, (2) experimental methods, (3) analog methods, and (4) numerical methods. Graphical, experimental, and analog methods are applicable to solving relatively few problems. Numerical methods have come into prominence and become more attractive with the advent of fast digital computers. The three most commonly used simple numerical techniques in EM are (1) moment method, (2) finite difference method, and (3) finite element method. Most EM problems involve either partial differential equations or integral equations. Partial differ- ential equations are usually solved using the finite difference method or the finite element method; integral equations are solved conveniently using the moment method. Although numerical methods give approximate solutions, the solutions are sufficiently accurate for engineering purposes. We should not get the impression that analytic techniques are out- dated because of numerical methods; rather they are complementary. As will be observed later, every numerical method involves an analytic simplification to the point where it is easy to apply the method. The Matlab codes developed for computer implementation of the concepts developed in this chapter are simplified and self-explanatory for instructional purposes. The notations 660
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15.2 FIELD PLOTTING 661 used in the programs are as close as possible to those used in the main text; some are defined wherever necessary. These programs are by no means unique; there are several ways of writing a computer program. Therefore, users may decide to modify the programs to suit their objectives.
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chapter 15 - Chapter 15 NUMERICAL METHODS The recipe for...

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