Numerical Calculations in Clifford Algebra

23Finite Difference Time Domain

The finite difference time domain (FDTD) method was introduced by Yee (1966) as a numerical method for simulating the propagation of electromagnetic waves. Of all methods for simulating electromagnetic wave propagation, this is the simplest to implement.

23.1 Theory

The propagation of electromagnetic waves was first described by Maxwell (1873a, 1873b). Written for a plane wave travelling in the direction within a uniform region of space void of sources, using a four‐dimensional Clifford number context with all negative signature, Maxwell's equations take the form of a single first‐order ordinary differential equation:

(23.1)

where:

(23.2)

The spatiotemporal differential operator is the Dirac (1928) operator, and the function is the electromagnetic field, as in Section 10.1.2. In this case, and are the magnetic and electric fields in the and ...