TABLE 45.1 Classification of Model Types in CEM Field Propagator escription Based on Integral operator Green's function for infinite medium or special boundaries Differential operator Maxwell curl equations or their integral counterparts Modal expansions Solutions of MaxwellI's equations in a particular coordinate system and expansion Rays and diffraction coefficients Application Determining the originating sources of a field and patte terns they produc Obtaining the fields distant from a known source Determining the perturbing effects of medium inhomogeneities onfiguration or wave number 1D, 2D, 3D Electrical properties of medium Dielectric, lossy, perfectly conducting, anisotropic, inhomogeneous, nonlinear, bianisotropic Linear, curved, segmented, compound, arbitrary TABLE 45.2 Steps in Developing a Computer Model Encapsulating observation and analysis in terms of elementary physical principles and their mathematical descriptions leshing out of the elementary description into a more complete, formally solved, mathematical representation umerical implementation Transforming into a computer algorithm using various numerical techniques Computation Obtaining quantitative results validation Determining the numerical and physical credibility of the computed results would include at a minimum those outlined in Table 45. 2. Note that by its nature, validation is an open-ended process that cumulatively can absorb more effort than all the other steps together. The primary focus of the following discussion is on the issue of numerical implementation. Desirable Attributes of a Computer Model A computer model must have some minimum set of basic properties to be useful From the long list of attributes rtant a summarized in Table 45.3. Accuracy is put foremost because results of insufficient or unknown accuracy have uncertain value and may even be harmful. On the other hand, a code that produces accurate results but at unacceptable cost will have hardly any more value. Finally, a code's applicability in terms of the depth and breadth of the problems for which it can be used determines its utility. The Role of Approximation As approximation is an intrinsic part of each step involved in developing a computer model, we summarize some of the more commonly used approximations in Table 45. 4. We note that the distinction between ar approximation at the conceptualization step and during the formulation is somewhat arbitrary, but choose to use the former category for those approximations that occur before the formulation itself. c 2000 by CRC Press LLC© 2000 by CRC Press LLC would include at a minimum those outlined in Table 45.2. Note that by its nature, validation is an open-ended process that cumulatively can absorb more effort than all the other steps together. The primary focus of the following discussion is on the issue of numerical implementation. Desirable Attributes of a Computer Model A computer model must have some minimum set of basic properties to be useful. From the long list of attributes that might be desired, we consider: (1) accuracy, (2) efficiency, and (3) utility the three most important as summarized in Table 45.3. Accuracy is put foremost because results of insufficient or unknown accuracy have uncertain value and may even be harmful. On the other hand, a code that produces accurate results but at unacceptable cost will have hardly any more value. Finally, a code’s applicability in terms of the depth and breadth of the problems for which it can be used determines its utility. The Role of Approximation As approximation is an intrinsic part of each step involved in developing a computer model, we summarize some of the more commonly used approximations in Table 45.4. We note that the distinction between an approximation at the conceptualization step and during the formulation is somewhat arbitrary, but choose to use the former category for those approximations that occur before the formulation itself. TABLE 45.1 Classification of Model Types in CEM Field Propagator Description Based on Integral operator Green’s function for infinite medium or special boundaries Differential operator Maxwell curl equations or their integral counterparts Modal expansions Solutions of Maxwell’s equations in a particular coordinate system and expansion Optical description Rays and diffraction coefficients Application Requires Radiation Determining the originating sources of a field and patterns they produce Propagation Obtaining the fields distant from a known source Scattering Determining the perturbing effects of medium inhomogeneities Problem type Characterized by Solution domain Time or frequency Solution space Configuration or wave number Dimensionality 1D, 2D, 3D Electrical properties of medium and/or boundary Dielectric, lossy, perfectly conducting, anisotropic, inhomogeneous, nonlinear, bianisotropic Boundary geometry Linear, curved, segmented, compound, arbitrary TABLE 45.2 Steps in Developing a Computer Model Step Activity Conceptualization Encapsulating observation and analysis in terms of elementary physical principles and their mathematical descriptions Formulation Fleshing out of the elementary description into a more complete, formally solved, mathematical representation Numerical implementation Transforming into a computer algorithm using various numerical techniques Computation Obtaining quantitative results Validation Determining the numerical and physical credibility of the computed results