Reliability analysis of N-equations N-unknowns method for the solution of the finite-difference time-domain (FDTD) problems

Abstract

Finite-difference time-domain (FDTD) solution of electromagnetic problems at high-frequency (HF) range is a challenging task. This is due to two requirements of accurate geometrical modeling for small objects/antennas and proper modeling of skin-depth effect. Generally, the fine meshes are used to overcome these problems. However, this leads to a large number of time iterations because of the small unit time step. To decrease the computational time, N-equations N-unknowns (NE-NU) method is developed for multi-frequency sources. Therefore, utilizing wideband nature of the FDTD method, NE-NU method is valuable. However, the reliability analysis of the NE-NU method has not been investigated in the literature. This study is the first numerical application of the NE-NU method that the reliability analysis of the NE-NU method is performed by using condition number calculation and it is validated by time-domain signals of an illustrative numerical example of a HF radar problem. A successful case and a failing case of the NE-NU method are clearly revealed. The effect of using a double-precision floating-point number and a single-precision floating-point number is also discussed. It is proved that a crucial value of the condition number can be found for the reliable NE-NU results.