Toward the 2-D Stable FDTD Subgridding Method With SBP-SAT and Arbitrary Grid Ratio

A provably stable summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method with arbitrary grid ratios is pro-posed to accurately and flexibly solve 2-D electromagnetic problems. The interpolation matrix with the grid ratio 1:n is first carefully designed, which satisfies the norm-compatible conditions and the SBP property to guarantee long-term stability. By introducing a virtual intermediate domain, the interpolation matrix with an arbitrary grid ratio n:m is decomposed into two interpolation matrices as n:1 and 1:m. By combining two interpolation matrices, the interpolation matrix with an arbi-trary grid ratio is derived, which is flexible to model complex structures. Five numerical examples were carried out to validate the effectiveness of the proposed SBP-SAT FDTD subgridding method with arbitrary grid ratios. Results show that it can flexibly model complex structures and significantly improve computational accuracy and efficiency.