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2007•Mathematical Models and Methods in Applied SciencesRequires access

GENERALIZED FORMULATIONS OF MAXWELL'S EQUATIONS FOR NUMERICAL VLASOV–MAXWELL SIMULATIONS

Régine Barthelmé, Patrick Ciarlet, Éric Sonnendrücker

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Abstract

When solving numerically approximations of the Vlasov–Maxwell equations, the source terms in Maxwell's equations coming from the numerical solution of the Vlasov equation do not generally satisfy the continuity equation which is required for Maxwell's equations to be well-posed. Hence it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. Different such formulations have been introduced previously. The aim of this paper is to perform their mathematical analysis and verify the existence and uniqueness of the solution.

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What this paper is about

When solving numerically approximations of the Vlasov–Maxwell equations, the source terms in Maxwell's equations coming from the numerical solution of the Vlasov equation do not generally satisfy the continuity equation which is required for Maxwell's equations to be well-posed. Hence it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. Different such formulations have been introduced previously. The aim of this paper is to perform their mathematical analysis and verify the existence and uniqueness of the solution.

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Available abstract

When solving numerically approximations of the Vlasov–Maxwell equations, the source terms in Maxwell's equations coming from the numerical solution of the Vlasov equation do not generally satisfy the continuity equation which is required for Maxwell's equations to be well-posed. Hence it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. Different such formulations have been introduced previously. The aim of this paper is to perform their mathematical analysis and verify the existence and uniqueness of the solution.

Key concepts: Maxwell's equations, Plasma modeling, Scattering-matrix method, Maxwell relations, Matrix representation of Maxwell's equations, Uniqueness, Electromagnetic field solver, Mathematics

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GENERALIZED FORMULATIONS OF MAXWELL'S EQUATIONS FOR NUMERICAL VLASOV–MAXWELL SIMULATIONS — Research Paper | ScholarLens