Numerical investigation of penalty factor for coulomb gauge of magnetic vector potential for 3D fields

In this paper, the penalty function method for constraining the Coulomb gauge of magnetic vector potential in the finite element analysis of 3-D magnetic field problems is introduced. The Galerkin method of weighted residual equations for the corresponding boundary value problems is derived. The numerical properties of the penalty factor are investigated using FEM modeling. These include the improvement of condition number of the FEM matrix equation system, satisfaction of divergence-free condition of the magnetic vector potential and the effect on the solution of the magnetic problem.