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 proposed 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 arbitrary 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.