Abstract A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by the simulation model using a variety of solvers. A scalability analysis is performed for both direct and preconditioned iterative solvers for four different pancakes solenoids with 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.