## ABSTRACT

This chapter presents some numerical techniques implemented in computational systems intended to simplify the finite element (FE) coding. It describes the modification of the N-Scheme technique for the employment in a non-stationary iterative solver. In order to validate the matrix-free procedure and to provide some timing results, a 2D electrostatic and two 3D magnetostatic cases are considered. The value of the relaxation factor is determined empirically and has proven to be a near-optimum choice for this problem configuration. Computations are performed conventionally with an assembled system matrix and matrix-free with the N-Scheme. When dealing with FE formulations that require numerical integrations to compute the elemental matrices, the CPU time to assemble the system matrix becomes prohibitively long, if the mesh contains a large number of elements. Timing results of an electrostatic test problem have provided a good first indication of the performance of the matrix-free algorithm.