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Computing the electric eddy currents in non-linear materials, such assuperconductors, is \E{not straightforward}. The design of superconductingmagnets and power applications needs electromagnetic computer modeling, beingin many cases a three-dimensional (3D) problem. Since 3D problems require highcomputing times, novel time-efficient modeling tools are highly desirable. Thisarticle presents a novel computing modeling method based on a variationalprinciple. The self-programmed implementation uses an original minimizationmethod, which divides the sample into sectors. This speeds-up the computationswith no loss of accuracy, while enabling efficient parallelization. This methodcould also be applied to model transients in linear materials or networks ofnon-linear electrical elements. As example, we analyze the magnetizationcurrents of a cubic superconductor. This 3D situation remains unknown, in spiteof the fact that it is often met in material characterization and bulkapplications. We found that below the penetration field and in part of thesample, current flux lines are not rectangular and significantly bend in thedirection parallel to the applied field. In conclusion, the presented numericalmethod is able to time-efficiently solve fully 3D situations without loss ofaccuracy.

3D computation of non-linear eddy currents: variational method and superconducting cubic bulk