An incomplete gauge formulation for 3D nodal finite-element magnetostatics

A method for imposing the gauge condition on the 3-D magnetic vector potential magnetostatic field computation using nodal finite elements is presented. In this method, the gauge A.w=0 is applied in the part of the problem that is not situated in the neighborhood of the materials interfaces that are tangential to w . This results in a formulation which maintains the discontinuous properties of the magnetic induction tangential components, reduces the number of unknowns, and improves the system matrix conditioning. The proposed formulation is compared with the Coulomb-gauge and ungauged formulations, showing that it results in better precision and worse conditioning than the Coulomb-gauge and has the same precision with a better conditioning than the ungauged formulation