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This study proposes an efficient method of local space-time grid refinement and examines the numerical stability and the accuracy of electromagnetic field analysis using the space-time finite-integration technique (FIT). The proposed subgrid method locally refines the space-time grid with three-division or four-division and is stable without inducing numerical instability even after one million time-steps. The grid construction is modified at the corner part of subgrid connection to improve the computational accuracy. The staircase-type grid relaxes the time-step restriction due to the CFL condition. [ABSTRACT FROM AUTHOR]