A Generalized Unit System for Concise Electromagnetic Formulation and Accurate Numerical Solutions

We present in this paper a novel generalized unit system (GUS) for electromagnetic formulation and for improving the numerical behavior of the solution procedure by decreasing the condition number of the finite element (FE) matrices. The goal is to express, in the GUS, the governing electromagnetic equations in a form that does not involve any factors such as 4π and those related to the physical properties of vacuum. This goal is achieved by scaling all physical quantities. The scaling factors are not all free parameters, but are constrained by specific relations. We prove that there are only two free parameters, but only one is significant for minimizing the condition number of the FE matrices. Numerical examples are presented to illustrate the essential features of the proposed GUS, including the minimization of the condition number.