A New Unconditionally Stable Scheme for FDTD Method Using Associated Hermite Orthogonal Functions

• Published in: IEEE transactions on antennas and propagation Vol. 62; no. 9; pp. 4804 - 4809
• Main Authors: Huang, Zheng-Yu, Shi, Li-Hua, Chen, Bin, Zhou, Ying-Hui
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Associated Hermite (AH) basis functions; Basis functions; electromagnetic field; Electromagnetic fields; Equations; Finite difference methods; finite difference time domain (FDTD); Finite difference time domain method; Finite element analysis; Magnetic fields; Mathematical analysis; Mathematical model; Mathematical models; Matrix decomposition; Orthogonal functions; Temporal logic; Time-domain analysis; Translations; unconditionally stable; Vectors
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2014.2327141

An unconditionally stable solution using associated Hermite (AH) functions is proposed for the finite-difference time-domain (FDTD) method. The electromagnetic fields and their time derivatives in time-domain Maxwell's equations are expanded by these orthonormal basis functions. By applying Galerkin temporal testing procedure to these expanded equations the time variable can be eliminated from the calculations. A set of implicit equations is derived to calculate the magnetic filed expansion coefficients of all orders of AH functions for the temporal variable. And the electrical field coefficients can be obtained respectively. With the appropriate translation and scale parameters, we can find a minimum-order basis functions subspace to approach a particular electromagnetic field. The numerical results have shown that the proposed method can reduce the CPU time to 0.59% of the traditional FDTD method while maintaining good accuracy.