A numerical code has been developed for analyzing the time evolution of the shielding current density in the high-temperature superconductor (HTS) bulk. In the code, the shielding current equations are discretized by means of the element-free Galerkin method and the resulting nonlinear system is solved by use of the pseudo Newton method with a variable relaxation factor. By means of the code, the shielding current density is calculated in cases where the ac current flows in a coil placed just above the HTS. The voltage induced in the coil is evaluated as a function of time and its spectral analysis is performed. The results of computations show a qualitative agreement with Mawatari's experimental results.