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We propose a technique to improve the stability of three-dimensional (3D) nonuniform mesh nonstandard FDTD (NS-FDTD) calculations. To mitigate the numerical instability arising from the connection of different-sized meshes, our method combines the usual interpolation fields and perfectly matched layer (PML) condition at mesh interfaces. We examine a connection for a mesh size ratio of 3:1, and show numerically that our technique improves the stability of 3D NS-FDTD calculation on nonuniform meshes. Our technique is also applied to analyze the fields around a periodic slot panel.