Acceleration of ADI-FDTD Method by Gauss-Seidel Relaxation Approach

Yuya NAKAZONO  Hideki ASAI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.2   pp.550-553
Publication Date: 2008/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.2.550
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Analog Circuit Techniques and Related Topics)
Category: 
Keyword: 
electromagnetic field analysis,  ADI-FDTD method,  relaxation method,  2-D simulation,  

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Summary: 
This report describes an application of relaxation technique to the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. The ADI-FDTD method is quite stable even when the CFL condition is not satisfied. However, the ADI-FDTD method is computationally more complicate than the conventional FDTD method and this method requires to solving the tri-diagonal matrix equation. Thus, this method may require more computational cost than the standard FDTD method due to the large scale tri-diagonal matrix solution corresponding to a large number of meshes. In this report, relaxation-based solution technique is discussed for the matrix solution and a simple numerical example is shown. As a result, it is confirmed that ADI-FDTD method with the relaxation technique is useful for the acceleration of the electromagnetic field simulation.