Method for solution of Maxwell's equations in non-uniform media

It is shown that the L₂ norm of electric currents induced in a dissipative medium can never exceed the norm of the external currents. This allows the construction of a simple iteration method to solve the Maxwell's equations. The method produces a series converging to the solution for an arbitrary conductivity distribution and arbitrary frequency of field variations. The convergence is slow if the lateral contrast of the conductivity distribution is about 10⁴ or higher. A modification significantly improving the convergence is described in this paper. As an example, electromagnetic fields induced in the model (including the western part of the Northern American continent and the adjacent part of the Pacific Ocean) are calculated.