A New Method to Solve 3-D Magnetodynamic Problems Without Assembling an $Ax=b$ System

In this paper, we present a technique to solve magnetodynamic finite-element method (FEM) cases where the assembling, storing, and solving the matrix system Ax=b is performed in a different way compared with the classical techniques. The application of this technique for static cases was already presented. Using the T-Ω formulation, we consider here eddy currents in the conductive parts of the domain using time stepping discretization. As main result, the implementation is much simpler than traditional techniques widely used in virtually all the FEM codes. The final results match the ones obtained by the classical methods with very good accuracy.