Abstract. We develop an adaptive finite element method for solving the eddy current model with voltage excitations for complicated three dimensional structures. The mathematical model is based on the A − φ formulation whose well-posedness is established. We derive the a posteriori error estimate for the finite element approximation of the model whose solution is not unique in the nonconducting region. Numerical experiments are provided which illustrate the competitive behavior of the proposed method.Key words. Eddy current, circuit/field coupling, adaptivity, a posteriori error analysis, PHG package.
AMS subject classifications. 65N30, 65N551. Introduction. There are tremendous interests in practical applications to develop efficient electromagnetic analysis tools that are capable of wide-band analysis of very complicated geometries of conductor, see e.g. Zhu et al [33], Kamon et al [19]. One example is the analysis of interconnects where accurate estimates of the coupling impedances of complicated three dimensional structures are important for determining final circuit speeds or functionality. The standard problem in this case consists of the determination of the equivalent parameters in the domains where the full Maxwell equations or the magneto-quasi-static problem must be solved (Rubinacci et al [29]). There are great efforts in the engineering literature to solve the problem based on the volume integral method, see e.g. Ruehli [30], Heeb and Ruehli [14], [33], and [19].In this paper we develop an adaptive finite element method for solving the magneto-quasi-static or eddy current model with voltage excitations for complicated three dimensional structures. The eddy current model with voltage or current excitations draws considerable attention in the literature, see e.g. Dular [13], Kettunen [17], [29], Bermudez et al [5], Hiptmair and Sterz [15]. The difficulty is the coupling of the global quantities such as the voltage and current with local quantities like electric and magnetic fields. Our approach in this paper to couple the local and global quantities is based on the A − φ model in [29] where an integral formulation of the model is developed.Let Ω be a simply connected bounded domain with a connected Lipschitz boundary Γ which contains the conducting region Ω c and the nonconducting region Ω nc = Ω\Ω c . The conducting body Ω c is fed by N external sinusoidal voltage generators
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