High-Precision Controllable-Stability Conformal Finite-Difference Time-Domain Method

This paper proposes a generalized and controllable-stability conformal method to address stability challenges inherent in conformal finite-difference time-domain (CFDTD) algorithms. A quantitative stability analysis framework is established by systematically investigating geometric parameters of conformal grids across computational domains. The proposed method improves grid stability by adjusting edge lengths to regulate the conformal area, while preserving geometric fidelity. Compared with the staircase approximation scheme, the proposed method achieves a 10.84% reduction in mean absolute error. In comparison to previous conformal approaches, it enhances stability through minor adjustments to the integration region while preserving the geometric structure, thereby achieving an effective balance between numerical stability and computational accuracy. It improves stability over DM methods and readily adapts to non-uniform grids and parallelization. Extensive numerical tests on various complex models demonstrate the method's enhanced stability and accuracy retention.