Integral equations via saddle point problems for time-harmonic Maxwell's equations

Authors:
Francis Collino;Bruno Despres
Affiliations:
INRIA, Domaine de Rocquencourt 78153 Le Chesnay, France and CERFACS, 42 avenue G. Coriolis 31057 Toulouse, France;Commissariat à l'Energie Atomique, BP12, 91680, Bruyeres le Chatel, Cedex, and Laboratoire Jacques Louis Lions, Universite Pierre et Marie Curie, 175 rue Chevaleret, 75013, Paris, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

We propose a new system of integral equations for the exterior time harmonic Maxwell's equation. This system is derived first from elementary manipulations of classical equations then by the minimization of a quadratic functional associated to incoming and outgoing electromagnetic waves. We analyze the inf-sup condition and various penalized problems related to this system. Then we prove that an iterative algorithm for the solution of the system of integral equations is convergent. Other numerical issues are also discussed.