This article is cited in 5 papers

Formalism of two potentials for the numerical solution of Maxwell's equations

A. N. Kudryavtsev^a, S. I. Trashkeev<sup>b

a</sup> Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Institutskaya ul. 4/1, Novosibirsk, 630090, Russia
^b Institute of Laser Physics, Siberian Branch, Russian Academy of Sciences, pr. Lavrent'eva 13/3, Novosibirsk, 630090, Russia

Abstract: A new formulation of Maxwell's equations based on the introduction of two vector and two scalar potentials is proposed. As a result, the electromagnetic field equations are written as a hyperbolic system that contains, in contrast to the original Maxwell system, only evolution equations and does not involve equations in the form of differential constraints. This makes the new equations especially convenient for the numerical simulation of electromagnetic processes. Specifically, they can be solved by applying powerful modern shock-capturing methods based on the approximation of spatial derivatives by upwind differences. The cases of an electromagnetic field in a vacuum and an inhomogeneous material are considered. Examples are given in which electromagnetic wave propagation is simulated by solving the formulated system of equations with the help of modern high-order accurate schemes.

Key words: computational electrodynamics, formalism of two potentials, numerical solution of hyperbolic systems of equations, shock-capturing schemes.

UDC: 519.634

Received: 10.07.2012
Revised: 06.05.2013

DOI: 10.7868/S0044466913110100

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:11, 1653–1663

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