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A robust and fast numerical course for investigating the magnetic levitation (maglev) performance of high-temperature superconductors (HTSs) is proposed and implemented via finite-element methods (FEMs) in this paper. This numerical course uses the magnetic vector potential as the state variable to establish the partial differential equations (PDEs) for governing the electromagnetic properties of 2-D simplified HTSs, a smoothed Bean-Kim's model of a critical state to describe the nonlinear constitutive law of HTSs, and the advanced algorithm of Jacobian-free Newton-Krylov (JFNK) to handle the nonlinear system of the FEM equation. After being tested, this homemade FEM model was applied to investigate the influence of various FEM parameters, e.g., the dimension of the computational domain, the prescribed tolerance for convergence, the coarseness of the mesh, and the time step, upon the precision of levitation/guidance force on an HTS bulk while moving in a nonuniform field generated by a permanent-magnet track. The most important findings through these studies are that the coarse choice of tolerance can cause the nonphysical phenomena such as the crossings in the force loops, and the numerical results are very robust against the dimension of the computational domain, the coarseness of the mesh, and the time step. Based on these findings, it was found that the time consumed for performing a typical cycle of levitation force calculation is merely a few seconds, making the application of this FEM model for optimizing the HTS maglev system very attractive.