45 Computational Electromagnetics Introduction Background Discussion Modeling as a Transfer Function.Some Issues Involved in Developing a Computer Model 45.3 Analytical Issues in Developing a Computer Selection of Solution Domain. Selection of Field P 45.4 Numerical Issues in Developing a Compute Sampling Functions. The Method of Moments 45.5 Some Practical Consideratio tegral Equation Modeling. Differential Modeling· Discussion· Sampling Requirement 45.6 Ways of Decreasing Computer Time 45.7 Validation, Error Checking, and Error Analysi EK. Miller Modeling Uncertainties. Validation and Error Checking Los Alamos National Laboratory 45.8 Concluding Remark 45.1 Introduction The continuing growth of computing resources is changing how we think about, formulate, solve, and interpret problems In electromagnetics as elsewhere, computational techniques are complementing the more traditional approaches of measurement and analysis to vastly broaden the breadth and depth of problems that are now quantifiable Computational electromagnetics( CEM)may be broadly defined as that branch of electromagnetics that intrinsically and routinely involves using a digital computer to obtain numerical results. with the evolu- tionary development of CEM during the past 20-plus years, the third tool of computational methods has been added to the two classical tools of experimental observation and mathematical analysis. This discussion reviews some of the basic issues involved in CEM and includes only the detail needed illustrate the central ideas involved. The underlying principles that unify the various modeling approaches used in electromagnetics are emphasized while avoiding most of the specifics that make them different. Listed roughout are representative, but not exhaustive, numbers of references that deal with various specialty aspect of CEM. For readers interested in broader, more general expositions, the well-known book on the moment method by Harrington [1968 ]; the books edited by Mittra [1973, 1975), Uslenghi [ 1978], and Strait[1980] the monographs by Stutzman and Thiele [1981], Popovic, et al. [1982], Moore and Pizer [1984], and Wang [1991]; and an IEEE Press reprint volume on the topic edited by Miller et al. [1991] are recommended, as i the article by Miller[ 1988] from which this material is excerpted This chapter is excerpted from E. K. Miller, "A selective survey of computational electromagnetics, "IEEE Trans. Antennas Propagat, voL. AP-36, Pp. 1281-1305, @1988 IEEE c 2000 by CRC Press LLC© 2000 by CRC Press LLC 45 Computational Electromagnetics 45.1 Introduction 45.2 Background Discussion Modeling as a Transfer Function • Some Issues Involved in Developing a Computer Model 45.3 Analytical Issues in Developing a Computer Model Selection of Solution Domain • Selection of Field Propagator 45.4 Numerical Issues in Developing a Computer Model Sampling Functions • The Method of Moments 45.5 Some Practical Considerations Integral Equation Modeling • Differential Equation Modeling • Discussion • Sampling Requirements 45.6 Ways of Decreasing Computer Time 45.7 Validation, Error Checking, and Error Analysis Modeling Uncertainties • Validation and Error Checking 45.8 Concluding Remarks 45.1 Introduction The continuing growth of computing resources is changing how we think about, formulate, solve, and interpret problems. In electromagnetics as elsewhere, computational techniques are complementing the more traditional approaches of measurement and analysis to vastly broaden the breadth and depth of problems that are now quantifiable. Computational electromagnetics (CEM) may be broadly defined as that branch of electromagnetics that intrinsically and routinely involves using a digital computer to obtain numerical results. With the evolu￾tionary development of CEM during the past 20-plus years, the third tool of computational methods has been added to the two classical tools of experimental observation and mathematical analysis. This discussion reviews some of the basic issues involved in CEM and includes only the detail needed to illustrate the central ideas involved. The underlying principles that unify the various modeling approaches used in electromagnetics are emphasized while avoiding most of the specifics that make them different. Listed throughout are representative, but not exhaustive, numbers of references that deal with various specialty aspects of CEM. For readers interested in broader, more general expositions, the well-known book on the moment method by Harrington [1968]; the books edited by Mittra [1973, 1975], Uslenghi [1978], and Strait [1980]; the monographs by Stutzman and Thiele [1981], Popovic, et al. [1982], Moore and Pizer [1984], and Wang [1991]; and an IEEE Press reprint volume on the topic edited by Miller et al. [1991] are recommended, as is the article by Miller [1988] from which this material is excerpted. This chapter is excerpted from E. K. Miller, “A selective survey of computational electromagnetics,” IEEE Trans. Antennas Propagat., vol. AP-36, pp. 1281–1305, ©1988 IEEE. E.K. Miller Los Alamos National Laboratory