ABSTRACT
This chapter introduces numerical electromagnetism through one-dimensional pulse and wave propagation. It reviews the analytic theory of one-dimensional electromagnetism. The time step is constrained by the Courant condition, an upper limit for physical validity and numerical stability. The chapter proceeds to one-dimensional scattering solutions for steady-state systems. The finite-element relationships reduce to a set of linear equations with complex variables to represent the amplitude and phase of field quantities. The equations can be solved by extensions of the matrix methods. The chapter reviews the theoretical basis complex-number material properties and the definition of perfectly absorbing boundaries for free-space simulations. It covers resonant solutions. These solutions apply to closed systems where reflection of waves at boundaries gives rise to constructive interference at particular frequencies. The chapter reviews the theory of driven circuits with inductance, capacitance, and resistance to illustrate resonance criteria and summarizes numerical root-finding methods to minimize the steps in the search.
