A stable FDTD subgridding scheme with SBP-SAT for transient TM analysis

We proposed a provably stable FDTD subgridding method for accurate and efficient transient electromagnetic analysis. In the proposed method, several field components are properly added to the boundaries of Yee's grid to make sure that the discrete operators meet the 2nd-order and 4th-order summation-by-parts (SBP) properties. Then, by incorporating the simultaneous approximation terms (SATs) into the finite-difference time-domain (FDTD) method, the proposed FDTD subgridding method mimics the energy estimate of the continuous Maxwell's equations at the semi-discrete level to guarantee its stability. Furthermore, to couple multiple mesh blocks with different mesh sizes, the interpolation matrices are also derived. The proposed FDTD subgridding method is accurate, efficient, easy to implement and integrate into the existing FDTD codes with only simple modifications. At last, four numerical examples with fine structures are carried out to validate the effectiveness of the proposed method.