A Novel 3-D Locally Isotropic Dispersion HIE-FDTD Scheme With Low Numerical Dispersion and High Precision

This article presents a high-precision locally isotropic dispersion (ID) hybrid implicitexplicit (HIE) finite-difference time-domain (FDTD) algorithm locally ID HIE-FDTD (LID-HIE-FDTD), which effectively reduces numerical dispersion errors. Unlike existing ID-FDTD algorithms-whether explicit, implicit, or hybrid-which apply the ID finite-difference (FD) scheme in all three directions, the proposed method applies it only in the direction constrained by stability conditions. It is theoretically proven that, for the HIE-FDTD method, this approach achieves the same numerical dispersion accuracy as applying the ID FD scheme in all three directions but with significantly lower computational complexity and improved efficiency. The proposed method ensures numerical dispersion isotropy by determining weighting factors and minimizes numerical dispersion errors using a scaling factor. Notably, this is the first study to explore the use of negative weighting factors and their impact on numerical dispersion, introducing a unique bisection-based approach to determine the weighting factors. This article includes detailed analyses of numerical dispersion, stability conditions, and the derivation of the iterative equation for the proposed method. Four numerical examples are provided to demonstrate the computational efficiency and accuracy of the LID-HIE-FDTD method, highlighting its significant advantages in solving phase-sensitive electromagnetic scattering problems. This method extends the applicability of ID approaches and establishes a foundation for addressing more complex challenges in electromagnetics.