45.2 Background discussion Electromagnetics is the scientific discipline that deals with electric and magnetic sources and the fields these sources produce in specified environments. Maxwell's equations provide the starting point for the study of electromagnetic problems, together with certain principles and theorems such as osition, reciprocity, equivalence, induction, duality, linearity, and uniqueness, derived therefrom [Stratton, 1941; Harrington, 1961] While a variety of specialized problems can be identified, a common ingredient of essentially all of them is that of establishing a quantitative relationship between a cause(forcing function or input) and its effect(the response or output), a relationship which we refer to as a field propagator, the computational characteristics of which are determined by the mathematical form used to describe it. Modeling as a Transfer Function The foregoing relationship may be viewed as a gener PROBLEM DESCRIPTION alized transfer function(see Fig. 45. 1)in which two (ELECTRICAL GEOMETRICAL) ysis or the direct problem, the input is known and the transfer function is derivable from the problem sp mined. For the case of the synthesis or inverse INPUT/ TRANSFER FUNCTION OUTPUT ification, with the output or response to be deter DERIVED FROM problem, two problem classes may be identified. The MAXWELL asier synthesis problem involves finding the input, EQUATIONS NEAR AND FAR given the output and transfer function, an example of which is that of determining the source voltages FIGURE 45. 1 The electromagnetic transfer function relates that produce an observed pattern for a known the input, output, and problem. antenna array. The more difficult synthesis problem itself separates into two problems. One is that of finding the transfer function, given the input and output,an cample of which is that of finding a source distribution that produces a given far field. The other and still more difficult is that of finding the object geometry that produces an observed scattered field from a known ting field. The latter problem is the most difficult of the three synthesis problems to solve because it is intrinsically transcendental and nonlinear Electromagnetic propagators are derived from a particular solution of Maxwells equations, as the cause mentioned above normally involves some specified or known excitation whose effect is to induce some to-be- determined response(e.g, a radar cross section, antenna radiation pattern). It therefore follows that the essence of electromagnetics is the study and determination of field propagators to thereby obtain an input-output transfer function for the problem of interest, and it follows that this is also the goal of CEM. Some Issues Involved in Developing a Computer Model We briefly consider here a classification of model types, the steps involved in developing a computer model, the desirable attributes of a computer model, and finally the role of approximation throughout the modeling process. Classification of Model Types It is convenient to classify solution techniques for electromagnetic modeling in terms of the field propagator that might be used, the anticipated application, and the problem type for which the model is intended to be ed, as is outlined in Table 45. 1. Selection of a field propagator in the form, for example, of the Maxwell curl equations, a Greens function, modal or spectral expansions, or an optical description is a necessary first step developing a solution to any electromagnetic problem. Development of a Computer Model Development of a computer model in electromagnetics or literally any other disciplinary activity can be decomposed into a small number of basic, generic steps. These steps might be described by different names but c 2000 by CRC Press LLC© 2000 by CRC Press LLC 45.2 Background Discussion Electromagnetics is the scientific discipline that deals with electric and magnetic sources and the fields these sources produce in specified environments. Maxwell’s equations provide the starting point for the study of electromagnetic problems, together with certain principles and theorems such as superposition, reciprocity, equivalence, induction, duality, linearity, and uniqueness, derived therefrom [Stratton, 1941; Harrington, 1961]. While a variety of specialized problems can be identified, a common ingredient of essentially all of them is that of establishing a quantitative relationship between a cause (forcing function or input) and its effect (the response or output), a relationship which we refer to as a field propagator, the computational characteristics of which are determined by the mathematical form used to describe it. Modeling as a Transfer Function The foregoing relationship may be viewed as a gener￾alized transfer function (see Fig. 45.1) in which two basic problem types become apparent. For the anal￾ysis or the direct problem, the input is known and the transfer function is derivable from the problem spec￾ification, with the output or response to be deter￾mined. For the case of the synthesis or inverse problem, two problem classes may be identified. The easier synthesis problem involves finding the input, given the output and transfer function, an example of which is that of determining the source voltages that produce an observed pattern for a known antenna array. The more difficult synthesis problem itself separates into two problems. One is that of finding the transfer function, given the input and output, an example of which is that of finding a source distribution that produces a given far field. The other and still more difficult is that of finding the object geometry that produces an observed scattered field from a known exciting field. The latter problem is the most difficult of the three synthesis problems to solve because it is intrinsically transcendental and nonlinear. Electromagnetic propagators are derived from a particular solution of Maxwell’s equations, as the cause mentioned above normally involves some specified or known excitation whose effect is to induce some to-be￾determined response (e.g., a radar cross section, antenna radiation pattern). It therefore follows that the essence of electromagnetics is the study and determination of field propagators to thereby obtain an input–output transfer function for the problem of interest, and it follows that this is also the goal of CEM. Some Issues Involved in Developing a Computer Model We briefly consider here a classification of model types, the steps involved in developing a computer model, the desirable attributes of a computer model, and finally the role of approximation throughout the modeling process. Classification of Model Types It is convenient to classify solution techniques for electromagnetic modeling in terms of the field propagator that might be used, the anticipated application, and the problem type for which the model is intended to be used, as is outlined in Table 45.1. Selection of a field propagator in the form, for example, of the Maxwell curl equations, a Green’s function, modal or spectral expansions, or an optical description is a necessary first step in developing a solution to any electromagnetic problem. Development of a Computer Model Development of a computer model in electromagnetics or literally any other disciplinary activity can be decomposed into a small number of basic, generic steps. These steps might be described by different names but FIGURE 45.1 The electromagnetic transfer function relates the input, output, and problem