Computational electromagnetics

Computational electromagnetics (CEM) is a natural extension of the analytical approach to solving the Maxwell equations [Elliott 1966]. This scientific discipline is based on numerically solving the governing partial differential or integral equations derived from first principles. In spite of a fundamental difference in representing the solution either in the continuum or in the discretized space, both approaches satisfy all pertaining theorems rigorously. Although numerical solutions of CEM generate only a point value for a specific simulation, the complexity of physics and of the field configuration are no longer the limiting factors as they are to the analytical approach. With the advent of high-performance computing systems, CEM is becoming the mainstay for engineering applications. Numerical simulation technology is the most cost-effective means of meeting many technical challenges in the areas of electromagnetic signature processing, antenna design, biomedical application, electromagnetic coupling, microwave device design and assembly. In fact, the military applications in radar signature reduction and integrated broadband communication system design have become the cutting edge of this relatively new technology. The technical transitions have already favorably influenced commercial ventures in telecommunications, magnetically levitated transportation systems, microwave data link optimization, and mobile antenna design, as well as microcircuit packaging. All computational electromagnetics methods also have limitations in their ability to duplicate physics in high fidelity. For a specific application, the numerical accuracy requirement has a direct connection to the computational efficiency. The inaccuracy incurred by a numerical simulation is attributable to the mathematical model of the physics, the numerical algorithm, and the computational accuracy. For example, in the electromagnetic signature simulations, the scattering-field formulation eliminates completely the quasiphysical error involved in the incident wave when it propagates from the far field boundary to the scatter. This accuracy advantage over the total-field formulation is significant by invoking the equivalent field theorem to accomplish the nearto far-field transformation. The computational accuracy is controlled by the algorithm and computing system adopted. Error induced by the discretization consists of the roundoff and the truncation error. The roundoff error is contributed by the computing system and is problem-size-dependent. Because this error behavior is random, it is the most difficult to evaluate. One anticipates that this type of error will be a concern for solving procedures involving large-scale matrix manipulation such as the method of moments [Harrington 1968] and the implicit numerical algorithm for finite-difference or finite-volume methods. The truncation error for time-dependent calculations appears as dissipation and dispersion, which can be assessed and alleviated by mesh system refinements. Finally, the numerical error can be the consequence of a specific numerical formulation. The error becomes pronounced when a special phenomenon is investigated or when a discontinuous and distinctive