Authors: Xikui Ma and Tianyu Dong
Source: FERMAT, Volume 19, Communication 15, Jan-Feb., 2017
Abstract: The finite-difference time-domain (FDTD) method is one of the most widely used full-wave electromagnetic simulation tools for solving Maxwell’s curl equations due to its simplicity, straightforwardness and easy implementation. However, the Courant-Friedrich-Levy (CFL) stability condition and the increasing numerical dispersion error have limited the intense utilization of the FDTD. Thus, the development of accurate and efficient numerical algorithms for solving Maxwell’s equations is still an attractive topic in our computational electromagnetics (CEM) society. The precise integration time domain (PITD) method is proposed for solving Maxwell’s equations, which breaks through the CFL limit and improves the computational efficiency. The fundamental idea of the PITD method consists of reducing Maxwell’s curl equations to a set of ordinary differential equations (ODEs) by approximating the spatial derivative with difference only, and solving the ODEs by using the precise integration (PI) technique with an accuracy of machinery precision. Compared to the convectional FDTD method, the PITD method posseses some striking features, which are summerized hereinafter.
Index Terms: computational electromagnetics, matrix-exponential methods, time-domain analysis, large time-steps, and precise integration technique.
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The Precise Integration Time Domain (PITD) Method - A Supplement to the Computational Electromagnetics