Numerical solution features of Maxwell equations by FDTD method in the homogeneous and nonhomogeneous formulations

Abstract

In this paper we investigate the features of the numerical
 FDTD solution of Maxwell’s equations formulated as Cauchy
 problems for the corresponding homogeneous and inhomogeneous
 systems of equations. It is shown that for the case
 of time-limited field sources the Cauchy problem for an inhomogeneous
 system is equivalent to the corresponding Cauchy
 problem for a homogeneous system. The criterion for evaluating
 the correctness of the obtained solution is defined. The
 features of the numerical solution of homogeneous and nonhomogeneous
 Cauchy problems for different forms of initial
 configurations of electromagnetic fields and setting pulses
 are analyzed. Necessary and sufficient conditions of correctness
 of the obtained solutions are formulated.