A 3-D finite element formulation for calculating Meissner currents in superconductors

A three-dimensional (3-D) finite element formulation for calculating Meissner currents in superconductors is presented. The authors have chosen a magnetic vector potential formulation, which also enables them to simulate ferromagnetic shielding. The equations are written so that the problem can be solved by the use of a conjugate gradient algorithm without preconditioning. Numerical results on normal-superconductor junctions and on superconducting lines are compared with analytical solutions.