  Computing the electric eddy currents in non-linear materials, such as
superconductors, is \E{not straightforward}. The design of superconducting
magnets and power applications needs electromagnetic computer modeling, being
in many cases a three-dimensional (3D) problem. Since 3D problems require high
computing times, novel time-efficient modeling tools are highly desirable. This
article presents a novel computing modeling method based on a variational
principle. The self-programmed implementation uses an original minimization
method, which divides the sample into sectors. This speeds-up the computations
with no loss of accuracy, while enabling efficient parallelization. This method
could also be applied to model transients in linear materials or networks of
non-linear electrical elements. As example, we analyze the magnetization
currents of a cubic superconductor. This 3D situation remains unknown, in spite
of the fact that it is often met in material characterization and bulk
applications. We found that below the penetration field and in part of the
sample, current flux lines are not rectangular and significantly bend in the
direction parallel to the applied field. In conclusion, the presented numerical
method is able to time-efficiently solve fully 3D situations without loss of
accuracy.
