Subgridding to Solving Magnetostatics Within Discrete Geometric Approach

We propose a recipe to construct a symmetric positive definite and consistent reluctance constitutive matrix to be used within discrete geometric approaches when the primal grid is generated by an enhanced subgridding of a generic hexahedral grid. We focus on a magnetostatic problem as working example.

I. Introduction

A discrete geometric approach (DGA) of electromagnetic field problems is at the base of the fundamental works of T. Weiland with the finite integration technique (FIT) [1]–[3], E. Tonti with the Cell method (CM) [4]–[6] and A. Bossavit [8]–[11], [13]–[15], where a direct way of discretizing Maxwell equations is presented, alternative to the classical Galerkin methods in finite elements.