Stability Analyses of Nonuniform Time-Step LOD-FDTD Methods for Electromagnetic and Thermal Simulations

This paper presents the stability analyses of nonuniform time-step (NUTS) locally one-dimensional finite-difference time-domain (LOD-FDTD) methods for electromagnetic (EM) and thermal simulations. The overall (spatial domain) transition matrix for the whole 3-D computational domain is considered for NUTS, which takes into consideration general inhomogeneous and lossy media. Rigorous stability analyses of NUTS LOD-FDTD methods are provided for both EM and thermal simulations. The analytical proofs of unconditional stability are performed through careful assertion of respective matrix definiteness, along with spectral radius and induced matrix norm analyses. Proper transformations and manipulations are carried out differently for EM and thermal analyses to suit different matrix properties. In each analysis, the fundamental form of the transition matrix is utilized with only one main inverse term, which results in much simpler and concise analysis. It is shown that the NUTS LOD-FDTD methods are unconditionally stable for both EM and thermal simulations.