研究目的
To derive the numerical dispersion relation for the finite-difference time-domain (FDTD) method applied to spherical grids, based on spherical wave functions, to accurately predict numerical behavior and errors.
研究成果
The derived numerical dispersion relation for spherical FDTD, based on spherical wave functions, accurately predicts numerical behavior and errors, including singularities at the origin and z-axis. This foundational work enables future numerical error and stability analysis.
研究不足
The study focuses on the theoretical derivation of the numerical dispersion relation and does not provide empirical validation or application examples. The complexity of spherical coordinates and the need for special update equations at singular points (origin and z-axis) may limit practical implementation.
