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Pre-Publicación 2010-16

Alfredo Bermúdez, Bibiana López-Rodríguez, Rodolfo Rodríguez, Pilar Salgado:

Numerical solution of transient eddy current problems with input current intensities as boundary data

Abstract:

The aim of this paper is to analyze a numerical method to solve transient eddy current problems with input current intensities as data, formulated in terms of the magnetic field in a bounded domain including conductors and dielectrics. To this end, we introduce a time-dependent weak formulation and prove its well-posedness. Under appropriate hypotheses on the input current intensities, we show that the weak solution has additional regularity and satisfies strong forms of the equations. We propose a finite element method for space discretization based on Nédélec edge elements on tetrahedral mesh, for which we prove well-posedness and error estimates. Furthermore, we introduce an implicit Euler scheme for time discretization and prove error estimates for the fully discrete problem. Moreover, a magnetic scalar potential is introduced to deal with the curl-free condition in the dielectric domain. This approach leads to an important saving in computational effort. Finally, the method is applied to solve two problems: a test with a known analytical solution and an application to electromagnetic forming.

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Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(s):

Alfredo BERMúDEZ, Bibiana LóPEZ-RODRíGUEZ, Rodolfo RODRíGUEZ, Pilar SALGADO: Numerical solution of transient eddy current problems with input current intensities as boundary data. IMA Journal of Numerical Analysis, vol. 32, 3, pp. 1001-1029, (2012).