Finite difference solution of EM fields by asymptotic waveform techniques

A new finite difference technique for the solution of electromagnetic (EM) field problems is presented. It is based on complex-frequency hopping (CFH), which is an expanded asymptotic waveform evaluation approach proposed in the circuit simulation area with great success in solving large linear lumped and distributed circuits. The Maxwell´s equations, as well as the special case-Helmholtz equations, are formulated into a set of linear ordinary differential equations by spatial finite difference, and the equations are solved by asymptotic waveform evaluation. The technique is guaranteed to be stable and offers potential speed up over existing finite difference approaches, for example, the finite difference frequency domain (FDFD) and the finite difference time domain (FDTD) for comparable accuracy. Examples of frequency-domain analysis of waveguides and dielectric cylinders are provided.