A characterization of singular electromagnetic fields by an inductive approach

Franck Assous, Patrick Ciarlet, Emmanuelle Garcia

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this article, we are interested in the mathematical modeling of singular electromagnetic fields, in a non-convex polyhedral domain. We first describe the local trace (i. e. defined on a face) of the normal derivative of an L2 function, with L2 Laplacian. Among other things, this allows us to describe dual singularities of the Laplace problem with homogeneous Neumann boundary condition. We then provide generalized integration by parts formulae for the Laplace, divergence and curl operators. With the help of these results, one can split electromagnetic fields into regular and singular parts, which are then characterized. We also study the particular case of divergence-free and curl-free fields, and provide non-orthogonal decompositions that are numerically computable.

Original languageEnglish
Pages (from-to)491-515
Number of pages25
JournalInternational Journal of Numerical Analysis and Modeling
Issue number3
StatePublished - 2008


  • Maxwell's equations
  • Polyhedral domains
  • Singular geometries


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