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We analyse a numerical method for the coupled system of the eddy currentequations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in abounded domain. The unbounded domain is discretised by means offinite-element/boundary-element coupling. Even though the considered problem isstrongly nonlinear, the numerical approach is constructed such that only twolinear systems per time step have to be solved. In this first part of thepaper, we prove unconditional weak convergence (of a subsequence) of thefinite-element solutions towards a weak solution. A priori error estimates willbe presented in the second part.

The Eddy Current-LLG Equations-Part I: FEM-BEM Coupling