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

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...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2013-11, Vol.53 (11), p.1653-1663
Main Authors: Kudryavtsev, A. N., Trashkeev, S. I.
Format: Article
Language:English
Subjects:
Approximation
Computational mathematics
Computational Mathematics and Numerical Analysis
Computer simulation
Derivatives
Differential equations
Electromagnetism
Magnetic fields
Mathematical models
Mathematics
Mathematics and Statistics
Physics
Propagation
Studies
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542513110079