An Unsymmetric FDTD Subgridding Algorithm With Unconditional Stability

To preserve accuracy in a grid with arbitrary subgrids, a finite-difference time-domain (FDTD) subgridding scheme, in general, would result in an unsymmetric numerical system. Such a numerical system can have complex-valued eigenvalues, which will render a traditional explicit time marching of FDTD absolutely unstable. In this paper, we develop an accurate FDTD subgridding algorithm suitable for arbitrary subgridding settings with arbitrary contrast ratios between the normal grid and the subgrid. Although the resulting system matrix is also unsymmetric, we develop a time-marching method to overcome the stability problem without sacrificing the matrix-free merit of the original FDTD. This method is general, which is also applicable to other subgridding algorithms whose underlying numerical systems are unsymmetric. The proposed FDTD subgridding algorithm is then further made unconditionally stable, thus permitting the use of a time step independent of space step. Extensive numerical experiments involving both 2- and 3-D subgrids with various contrast ratios have demonstrated the accuracy, stability, and efficiency of the proposed subgridding algorithm.