Computational Electromagnetics - Maxwell's Equations in Hyperbolic PDE Form

Maxwell's Equations in Hyperbolic PDE Form

Maxwell's equations can be formulated as a hyperbolic system of partial differential equations. This gives access to powerful techniques for numerical solutions.

It is assumed that the waves propagate in the (x,y)-plane and restrict the direction of the magnetic field to be parallel to the z-axis and thus the electric field to be parallel to the (x,y) plane. The wave is called a transverse electric (TE) wave. In 2D and no polarization terms present, Maxwell's equations can then be formulated as:

where u, A, B, and C are defined as