An Explicit Newmark-FDTD Algorithm With Subgridding Technique

We address the electromagnetic problem involving small structures, and put forward an improved, explicit finite-difference time-domain (FDTD) algorithm based on the Newmark discretization with subgridding technique. This algorithm achieves a stable, low-reflection, and straightforward subgridding with an arbitrary grid refinement ratio by adopting hanging variables. The Newmark method is employed to discretize the numerical system generated by the subgridding method. Besides, the Neumann series is used to obtain the inverse of the coefficient matrix. It makes the time-marching explicit and stable with a uniform large time step only determined by the coarse grid size in the whole computational domain. The series expansion avoids the matrix inversion operation, which largely enhances the calculation efficiency compared to the traditional Newmark-FDTD method. Numerical results prove the reliability and robustness of the proposed method.