PART I: INTEGRAL-EQUATION MODELING
The reciprocity theorem for transient diffusive electromagnetic fields is taken as the point of departure for developing computational methods to model such fields. Mathematically, the theorem is representative of any weak formulation of the field problem. Physically, the theorem describes the interaction between (a discretized version of) the actual field and a suitably chosen computational state. The choice of the computational state determines which type of computational method results from the analysis. It is shown that the finite-element method, the integral-equation method, and the domain-integration method can be viewed as particular cases of discretization of the reciprocity relation. The local field representations of the electric- and the magnetic-field strengths in terms of edge-element expansion functions are worked out in some detail.
The emphasis is on time-domain methods. The relationship with complex frequency-domain methods is indicated and used to symmetrize the basic field equations. This symmetrization expresses the correspondence that exists between transient electromagnetic wavefields in lossless media and transient diffusive electromagnetic fields in conductive media where the electric displacement-current contribution to the field can be neglected in the time window of observation. This aspect is also of importance in numerical modeling.