On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

The effects of finite-element grid geometries and associated ill conditioning were studied in single-medium and multimedia (air-iron) three-dimensional magnetostatic-field computation problems. The sensitivities of these 3-D field computations to finite-element grid geometries were investigated. It was found that in single-medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first-order finite elements produces global results which are almost totally insensitive to grid geometries. However, it was found that in multimedia (air-iron) applications first-order finite-element results are sensitive to grid geometries and consequent elemental shape ill conditioning. These sensitivities were almost totally eliminated by the use of second-order finite elements in the field-computation algorithms. Practical examples are given to demonstrate these findings.>