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

Authors:
Bengt Fornberg;Julia Zuev;Jongwoo Lee
Affiliations:
University of Colorado, Department of Applied Mathematics, 526 UCB, Boulder, CO80309, USA;University of Colorado, Department of Applied Mathematics, 526 UCB, Boulder, CO80309, USA;Kwangwoon University, Department of Mathematics, 447-1 Wolgye-Dong, Nowon-Gu, Seoul 139-701, Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

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.