Abstract:Having in mind the modeling of induction heating systems (see, for instance, [1]), we analyze a time-harmonic eddy current model in an axisymmetric three-dimensional domain.
For this problem, we propose a symmetric FEM and BEM coupling method in terms of a magnetic vector potential. More precisely, we write a weak formulation in suitable weighted Sobolev spaces and follow some techniques of [1,2] to prove that this formulation is well-posed. We also propose a discretization that leads to a Galerkin scheme, that we show is convergent and has an optimal order of convergence.
We underline that [2] deals with the problem in the bounded case, whereas both [1] and our work consider an unbounded situacion. Besides, on the contrary to [1], the coupling procedure that we propose is of symmetric kind, in order to allow the analysis of the BEM-FEM formulation and its discretization even for realistic boundaries.
(Joint work with P. Salgado.)
References:
[1] A. Bermúdez, D. Gómez, M.C. Muñiz, P. Salgado, R. Vázquez. Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace. Applied Numerical Mathematics 59 (2009), 2082-2104.
[2] A. Bermúdez, C. Reales, R. Rodríguez, P. Salgado, Numerical analysis of a finite element method for the axisymmetric eddy current model of an induction furnace. IMA Journal of Numerical Analysis 30 (2010), 654-676.