A COURSE IN COMPUTATIONAL ELECTROSTATIC FIELD THEORY

There are many textbooks in electromagnetic …eld theory. Some are very mathematical and emphasize the closed form analyses of problems utilizing Maxwell’s equations. These closed form mathematical solutions yield solu- tions to any desired accuracy. When simple enough they may provide phys- ical insight. Most often these solutions require summations and integration of various tabulated functions and sometimes require the calculation of new functions. In such cases getting numerical results can require a great deal of calculation and care to insure the convergence of various series and/or the solution of many simultaneous equations. For these reasons many ad- vanced courses in electromagnetic problem solving degenerate into exercises in advanced mathematics. Sometimes physical understanding of electric and magnetic phenomena is obscured in a fog of Bessel, Hankel, Struve etc. func- tions. It has been said that almost any electromagnetic problem that can be solved analytically appears in textbooks and journals. In the past it has been necessary at times for professors to prevent students from accessing those solutions by borrowing them from all the local libraries. It is a lot of work and not always possible. With the advent of the internet it may be an impossible task to get students to solve these old problems by their own e¤orts. The seasoned professor knows any change in the geometry of the problems solved in the literature can make them almost impossible to solve in closed form. The goal of this book is to enable students by the use of …nite element analysis to solve the problems that could not be solved analytically. The readers accomplish this without having to devise their own …nite element programs for each di¤erent problem. Being able to quickly get solutions to new problems in one, two and three dimensional space and make changes in them leads more quickly to physical understanding than spending hours working with complex mathematics. Numerous commercially available …nite element, …nite di¤erence and bound- ary element programs are available for varying prices. Some are even free, for example the Poisson Super…sh software of the Los Almos National Labora- tory. Poisson Super…sh is a collection of programs for calculating static mag- netic and electric …elds and radio-frequency electromagnetic …elds in either 2- D Cartesian coordinates or axially symmetric cylindrical coordinates. It can be down loaded fromhttp://laacg1.lanl.gov/laacg/services/download_sf.phtml at no cost. A lengthy list of some of the available software is given at http://emclab.mst.edu/csoft.html. In much of the available software codes are given for certain types of problems only and do not allow the user to specify his own partial di¤erential equations. The authors use and study of many of these codes has resulted in his preference for FlexPDE available at www.pdesolutions.com. It is available at many universities and student versions are free. FlexPDE can solve any number of simultaneous partial di¤erential equations that are second order in space and …rst order in time and operates in one, two and three dimensions.