Piecewise Calculation Scheme for the Unconditionally Stable Chebyshev Finite-Difference Time-Domain Method

The unconditionally stable (US) Chebyshev (CS) finite-difference time-domain (FDTD) method is extended for solving the problems of long-time simulation or harmonic resonance using a piecewise calculation scheme. First, the CS differential matrix is derived from the inversion of integral matrix with...

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Bibliographic Details
Published in:IEEE transactions on microwave theory and techniques 2025-01, p.1-9
Main Authors: Huang, Zheng-Yu, Zheng, Xue-Qi, Chao-Li, Tan, Eng Leong, Chen, Zi-an, Shi, Li-Hua, Chen, Bin
Format: Article
Language:English
Subjects:
Chebyshev (CS) polynomials
Chebyshev approximation
Electromagnetic fields
Finite difference methods
finite-difference time-domain (FDTD)
Mathematical models
Maxwell equations
Microwave imaging
Microwave photonics
piecewise calculation
Polynomials
Time-domain analysis
Translation
unconditionally stable (US)
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Summary:The unconditionally stable (US) Chebyshev (CS) finite-difference time-domain (FDTD) method is extended for solving the problems of long-time simulation or harmonic resonance using a piecewise calculation scheme. First, the CS differential matrix is derived from the inversion of integral matrix with the differential characteristic of the CS polynomials. Then, the 2-D CS FDTD formula with initial values is derived based on the CS differential matrix, highlighting the merits of a closed interval for the CS basis functions and the 0th-order CS polynomial. In addition, the time-frequency support of CS functions for order selection is discussed. Finally, based on the above derivation, a piecewise calculation scheme is proposed to simulate an entire time, where the electromagnetic field is reconstructed piecewise with the Clenshaw law. Numerical examples for the 2-D {\rm TE}_z case show that the proposed method agrees well with the conventional FDTD method with the relative difference lower than -50 dB. This represents a higher accuracy than the associated hermite (AH) FDTD method and reduces the memory compared with the original CS FDTD method.
ISSN:0018-9480
1557-9670
DOI:10.1109/TMTT.2025.3532330