Implementing tri-potential approach in EMAP3D

The Institute for Advanced Technology, The University of Texas at Austin has developed the finite element code EMAP3D which is capable of modeling coupled mechanical, thermal and electromagnetic diffusive processes with moving conductors. The Lagrangian dual potential formulation (magnetic vector potential and electrical scalar potential) was used in the earlier version of EMAP3D because it has the desirable property of being single-valued in multiply-connected regions. Using the magnetic vector potential for nonconducting regions requires solving for three unknowns at each node and results in large storage requirements and high computing cost. An alternative is to use the magnetic scalar potential, the third potential in the tri-potential formulation, in nonconducting regions. This requires solving for only one unknown at each node in nonconducting regions; however, the magnetic scalar potential is not single-valued in multiply-connected regions and the user is required to define appropriate branch cuts. A detailed Lagrangian tri-potential formulation is presented and compared to the dual potential formulation through the simulation of a typical railgun problem. The tri-potential approach shows distinct advantages in terms of model size, computing cost, and solution accuracy.