A　finite-difference　time-domain　(FDTD)　subgridding　method　is　proposed　to　efficiently　and　accurately　solve　three-dimensional　electromagnetic　problems.　Based　on　the　reciprocal　and　symmetric　interpolation　operators　between　coarse　and　subgridding　meshes,　spatial　coupling　matrices　are　carefully　designed　to　guarantee　long-time　stability.　To　further　enhance　its　capability　of　handling　multiscale　structures,　arbitrary　grid　ratios　and　nested　subgridding　meshes　are　extended　to　be　supported　in　the　proposed　method.　In　addition,　the　rigorous　analysis　shows　that　the　proposed　FDTD　subgridding　method　is　theoretically　stable.　Five　numerical　examples　including　a　simple　cavity　with　perfect　electric　conductors,　a　rectangular　TEM　waveguide,　a　dielectric　resonator,　a　single-layer　substrate　integrated　waveguide,　and　a　large　airplane　platform　with　a　dipole　are　carried　out　to　validate　its　effectiveness.　Results　show　that　it　is　stable,　accurate,　efficient,　and　easy　to　model　complex　structures.　IEEE