Computer techniques for the modelling of complex electromagnetic interactions are explored. The main thesis is that these techniques, or methods, can be divided into two types:​ non-algorithmic and algorithmic techniques. Approximate algorithmic methods for the modelling of electromagnetic interactions have undergone great advances in the past twenty years but they are still only feasible for relatively small problems (i.e. where the space-time discretization produces and requires only a relatively small number of unknowns). The computer implementation of non-algorithmic methods have recently become a reality with the maturing of expert system technology and knowledge based engineering.

In Part I of this thesis, a knowledge-based approach for the modelling of electromagnetic (EM) interactions in a system is described. The purpose is to determine any unwanted EM effects which could jeopardize the safety and operation of the system. Modelling the interactions in a system requires the examination of the compounded and propagated effects of the electromagnetic fields. A useful EM modelling approach is one which is incremental and constraint-based. The approach taken here subdivides the modelling task into two parts:​

1. the definition of the related physical topology, and
2. the propagation of the electromagnetic constraints.

A prototype of some of the EM constraints has been implemented in Quintus Prolog under NeWS on a Sun workstation. User interaction is through a topology drawing tool and a stack-based attribute interface similar to the HyperCard™ interface of the Apple Macintosh computer.

In Part II, numerical methods which discretize the space-time region of interest and provide a solution to the electromagnetics problem, given appropriate initial and boundary conditions, are investigated. Specifically, time-domain finite difference methods as applied to Maxwell's equations are analyzed, compared and implemented. As the basis of this analysis, Maxwell's equations are expressed as a system of hyperbolic conservation laws. Analytical properties of these systems, based on the method of characteristics, are used to study the numerical solution of Maxwell's equations.

Practical issues, such as computational efficiency and memory requirements, are discussed for the implementation of the finite difference schemes. Advanced programming techniques are used to implement all the finite difference schemes discussed. The schemes are used to solve the problem of the penetration of electromagnetic energy through a shield with a thick gap.

A two-dimensional time-domain finite element method, implemented as the software package PDE/PROTRAN, is also applied to shielding problems. The software package is first validated for simple hyperbolic problems and is then applied to perfectly conducting shields with apertures.