Preliminary thinking about the mathematic foundation of modern computational electromagnetism

Abstract

Computation of time-dependent electromagnetic field excited by a varying current distribution is the hardcore of modern computational electromagnetism. However, differing from other computing forms of field problem described by partial differential equations, the computation of electromagnetic field did not really use series of the general, abstract and formalized methods. And people have to construct forms of different models to make computation. Such a method of computation can also arrange forms particular propositions suitably. But, it cannot be regarded as a universal method and it is usually implicates some logic mistakes and physical distortion. The reason would be: time-dependent electromagnetic field lacks of a united mathematical physical model that can guarantee both the partial differential equations and boundary conditions consistent in logic. In reverse, if a general mathematical model is perfect in logic, it can not only allow us to effectively use the computation methods supplied by computational mathematics but also provide more full and more exact information about electromagnetic field.