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Two special notes on the implementation of the unconditionally stable ADI‐FDTD method
Author(s) -
Zhao An Ping
Publication year - 2002
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.10295
Subject(s) - tridiagonal matrix , finite difference time domain method , alternating direction implicit method , tridiagonal matrix algorithm , matrix (chemical analysis) , mathematics , crank–nicolson method , finite difference method , simple (philosophy) , algorithm , computer science , mathematical analysis , physics , eigenvalues and eigenvectors , quantum mechanics , materials science , composite material , philosophy , epistemology
In this article two special considerations or notes on the implementation of the alternating direction implicit finite‐difference–time‐domain (ADI‐FDTD) method are discussed. In particular, the two notes are (a) the mathematical algorithm used to solve the tridiagonal matrix equation, and (b) the way to apply the excitation. First, it is found that the ADI‐FDTD method is not always stable if the algorithm (for solving the tridiagonal matrix equation) proposed in the book Numerical Recipes in C is adopted. Consequently, a simple, efficient, and stable mathematical algorithm for solving the tridiagonal matrix equation of the ADI‐FDTD method is presented. Second, it is demonstrated that, to obtain more accurate results for all the field components, the excitation function should be applied to both the first subiteration and the second subiteration, rather than forced in the first subiteration only. The theory proposed in this article is validated through numerical examples. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 273–277, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10295