Curl-free positive definite form of time-harmonic Maxwell’s equations well-suitable for iterative numerical solving

Abstract

A new form of time-harmonic Maxwell’s equations is developed on the base of the standard ones and proposed for numerical modeling. It is written for the magnetic field strength H, electric displacement D, vector potential A and the scalar potential Φ. There are several attractive features of this form. The 1st one is that the differential operator acting on these quantities is positive. The 2nd is absence of curl operators among the leading order differential operators. The Laplacian stands for leading order operator in the equations for H, A and Φ, while the gradient of divergence stands for D. The 3rd feature is absence of space varied coefficients in the leading order differential operators that provides diagonal domination of the resulting matrix of the discretized equations. A simple example is given to demonstrate the applicability of this new form of time-harmonic Maxwell’s equations.