Stability and accuracy of time-extrapolated ADI-FDTD methods for solving wave equations

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• 作者：Bengt Fornberg ; Julia Zuev ; Jongwoo Lee
• 关键词：Wave equations ; Maxwell's equations ; GBS method ; Extrapolation methods ; Stability domains ; ADI-FDTD
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2007
• 出版时间：1 March 2007
• 年：2007
• 卷：200
• 期：1
• 页码：178-192
• 全文大小：312 K

文摘

Some recent work on the ADI-FDTD method for solving Maxwell's equations in 3-D have brought out the importance of extrapolation methods for the time stepping of wave equations. Such extrapolation methods have previously been used for the solution of ODEs. The present context (of wave equations) brings up two main questions which have not been addressed previously: (1) when will extrapolation in time of an unconditionally stable scheme for a wave equation again feature unconditional stability, and (2) how will the accuracy and computational efficiency depend on how frequently in time the extrapolations are carried out. We analyze these issues here.