Kirchhoff's Laws as a Finite Volume Method for the Planar Maxwell Equations

Beginning with Maxwell's equations for the (
H
₁
,
H
₂
,
E
) polarized mode in an inhomogeneous planar medium, we derive a finite volume method that we recognize as Kirchhoff's laws for a corresponding circuit consisting of inductors, capacitors, and resistors. This association automatically gives local charge and energy conservation. The method is implemented and used to find the steady-state solution for two test problems. By comparison with the exact solution for the homogeneous medium problem, the method is shown to be linearly convergent.