×

Accurate extrapolation to zero cell size by Padé approximation. (English) Zbl 1015.78018

Summary: It is shown that extrapolation to zero cell size can be made accurately by means of Padé approximation. The extrapolation procedure is tested on waveguide cavity filters analysed by the finite difference-time domain (FDTD) scheme. Extrapolation by the traditional Taylor series can yield unphysical results in the vicinity of resonances where it is outperformed by extrapolation based on the Padé approximation. Direct computation with the FDTD scheme (without extrapolation) requires extreme and infeasible resolutions to achieve a reasonable accuracy close to resonances.

MSC:

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
65B05 Extrapolation to the limit, deferred corrections
41A21 Padé approximation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Transactions on Antennas and Propagation 14 pp 302– (1996)
[2] Taflove A Computational Electrodynamics: The Finite-Difference Time-Domain Method Artech House Norwood
[3] Weily, Microwave filters with improved spurious performance based on sandwiched conductor dielectric resonators, IEEE Transactions on Microwave Theory and Techniques 49 (9) pp 1501– (2001)
[4] Rylander, Stability of explicit-implicit hybrid time-stepping schemes for Maxwell’s equations, Journal of Computational Physics 179 (2) pp 426– (2002) · Zbl 1003.78010
[5] Heath TM Scientific Computing: An Introductory Survey McGraw-Hill New York 258 260
[6] Press W Teukolsky SA Vetterling WT Flannery BP Numerical Recipes in C: The Art of Scientific Computing 2nd edn Cambridge University Press New York
[7] Pillage, Asymptotic waveform evaluation for timing analysis, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 9 (4) pp 352– (1990) · Zbl 05449289
[8] Miller, Model-based parameter estimation in electromagnetics: Part I. background and theoretical development, IEEE Antennas and Propagation Magazine 40 (1) pp 42– (1998)
[9] Jin JM The Finite Element Method in Electromagnetics Wiley New York
[10] Rylander, Stable FEM-FDTD hybrid method for Maxwell’s equations, Computer Physics Communications 125 pp 75– (2000) · Zbl 1003.78009
[11] De Smedt, Electric singularity near the tip of a sharp cone, IEEE Transactions on Antennas and Propagation 36 (1) pp 152– (1988) · Zbl 0947.78516
[12] Alimenti, A revised formulation of model absorbing and matched modal source boundary conditions for the efficient FDTD analysis of waveguide structures, IEEE Transactions on Microwave Theory and Techniques 48 (1) pp 50– (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.