  A mathematical model for the charging simulation of non-insulated
superconducting pancake solenoids is presented. Numerical solutions are
obtained by the simulation model implemented on the Petra-M FEM platform using
a variety of solvers. A scalability analysis is performed for both direct and
preconditioned iterative solvers for four different pancakes solenoids with a
varying number of turns and mesh elements. It is found that even with two
extremely different time scales in the system an iterative solver combination
(FGMRES-GMRES) in conjunction with the parallel Auxiliary Space Maxwell Solver
(AMS) preconditioner outperforms a parallelized direct solver (MUMPS). In
general, the computational time of the iterative solver is found to increase
with the number of turns in the solenoids and/or the conductivity assumed for
the superconducting material.
