With recent technological advancements, antenna elements have become smaller whereas the platforms they operate on, e.g., helicopter airframes, become electrically larger. These problems yield large computational domains and require significant computational resources. Traditional finite methods (FDTD and FEM) are second-order accurate thereby restricting the size of the domains that can be handled efficiently. We propose an approach which combines a subgridding technique with a higher-order scheme. FDTD subgridding techniques divide the simulation space into two separate grids; a fine one and a coarse one. The standard FDTD(2,2) is used to handle any of the fine features of the structure, whereas on the coarse grid FDTD(2,4), which is second-order accurate in time and fourth-order accurate in space, is used. Thus existing successfully-applied techniques in FDTD(2,2) are available for use on the fine grid. On the coarse mesh, away from phenomena associated with the complex structure, FDTD(2,4) is used mainly to simulate wave propagation in homogeneous media. With this approach, high accuracy is obtained both around fine geometric features, such as thin wires, thin slots, etc., as well as in the wave propagation.