HIGHER-ORDER 3D-ISOPARAMETRIC FINITE-ELEMENTS FOR IMPROVED MAGNETIC-FIELD CALCULATION ACCURACY

The formulation and application of second order isoparametric three dimensional magnetic vector potential finite elements is described. For a hexahedral finite element, detailed expressions are derived for all of the shape functions and their derivatives. A patch test is passed by hexahedrons of both first and second orders. An extremely coarse mesh of both element orders is used to model the pathological problem of a closed steel loop deformed in three-dimensional space. The first order elements are shown to give only 2.4 percent of the correct magnetic field B in the steel, while the second order elements are shown to give 80 to 96 percent of the correct magnetic field.