Geodesic
Ultra-Weak Variational Formulation and efficient Integral Representation in Electromagnetism: a thorough study of the algorithm complexity
E. Darrigrand1
1 IRMAR - Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France
ESAIM. Proceedings, Tome 22 (2008), pp. 190-197.

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Many different methods have been developed for the solution of the time-harmonic Maxwell equations in exterior domains at high frequency. Volume based methods have the drawback of needing an artificial boundary far from the obstacle. Integral formulations enable one to avoid this difficulty by solving a problem on the surface of the obstacle, but imply dense systems with bad condition numbers. In this paper we study a coupling of the Ultra-Weak Variational Formulation (UWVF), a volume based method using plane wave basis functions, and an integral representation of the unknown field to obtain an exact artificial boundary condition. More precisely, we detail the study of the complexity of the new algorithm considering a 1-level or multilevel Fast Multipole Method.
DOI : 10.1051/proc:072224

E. Darrigrand 1

1 IRMAR - Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France 
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E. Darrigrand. Ultra-Weak Variational Formulation and efficient Integral Representation in Electromagnetism: a thorough study of the algorithm complexity. ESAIM. Proceedings, Tome 22 (2008), pp. 190-197. doi : 10.1051/proc:072224. http://geodesic.mathdoc.fr/articles/10.1051/proc:072224/

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