Reinterpreting Four-Stage Split-Step FDTD Methods as Two-Stage Methods

Grande, A.; Pereda, José Antonio Martín; Serroukh, Abdelaziz; Barba, I.; Cabeceira, A.C.L.; Represa, J.

doi:10.1109/tap.2013.2276930

Cited by 5 publications

(8 citation statements)

References 13 publications

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“…where E CN-TMz can be obtained by particularizing (5) for the TM z case and E LOD-TM z contains the error terms unique to the TM z -LOD-FDTD scheme. The error for the TM z case can thus be written as [13] T…”

Section: Lod-fdtd Scheme 1) Three Dimensional Casementioning

confidence: 99%

Accuracy Limitations of the Locally One-Dimensional FDTD Technique

Grande

Pereda

2014

Antennas Wirel. Propag. Lett.

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While the alternating-direction implicit finitedifference time-domain (ADI-FDTD) method preserves the second-order temporal accuracy of the conventional FDTD technique, the locally one-dimensional (LOD)-FDTD method exhibits a first-order in time splitting error. Despite this difference, the numerical dispersion analyses of these methods reveal that both present similar accuracy properties. For this reason, the characteristic non-commutativity error of the LOD-FDTD scheme has not received much attention. In this work, we determine the closed form of the local truncation error for the 3D-LOD-FDTD scheme. We find that it presents error terms which depend on the time-step size multiplied by the spatial derivatives of the fields. Numerical results confirm that these terms become a significant source of error which is not revealed in the dispersion analyses.

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Section: Lod-fdtd Scheme 1) Three Dimensional Casementioning

confidence: 99%

Accuracy Limitations of the Locally One-Dimensional FDTD Technique

Grande

Pereda

2014

Antennas Wirel. Propag. Lett.

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“…Naturally, second order in time can be ensured via Strang splitting (Lee and Fornberg, 2003), while more complex split-step alternatives may exhibit better features (Chu and Kong, 2009a, b). The equivalence of some of seemingly different approaches has been proved recently (Grande et al, 2013). Other authors have proposed the improvement of spatial accuracy via high-order operators (Fu and Tan, 2005;Liu et al, 2009).…”

Section: Introductionmentioning

confidence: 95%

Accelerated unconditionally stable FDTD scheme with modified operators

Zygiridis

Pyrialakos

Kantartzis

et al. 2015

COMPEL

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Purpose -The locally one-dimensional (LOD) finite-difference time-domain (FDTD) method features unconditional stability, yet its low accuracy in time can potentially become detrimental. Regarding the improvement of the method's reliability, existing solutions introduce high-order spatial operators, which nevertheless cannot deal with the augmented temporal errors. The purpose of the paper is to describe a systematic procedure that enables the efficient implementation of extended spatial stencils in the context of the LOD-FDTD scheme, capable of reducing the combined space-time flaws without additional computational cost. Design/methodology/approach -To accomplish the goal, the authors introduce spatial derivative approximations in parametric form, and then construct error formulae from the update equations, once they are represented as a one-stage process. The unknown operators are determined with the aid of two error-minimization procedures, which equally suppress errors both in space and time. Furthermore, accelerated implementation of the scheme is accomplished via parallelization on a graphics-processingunit (GPU), which greatly shortens the duration of implicit updates. Findings -It is shown that the performance of the LOD-FDTD method can be improved significantly, if it is properly modified according to accuracy-preserving principles. In addition, the numerical results verify that a GPU implementation of the implicit solver can result in up to 100× acceleration. Overall, the formulation developed herein describes a fast, unconditionally stable technique that remains reliable, even at coarse temporal resolutions. Originality/value -Dispersion-relation-preserving optimization is applied to an unconditionally stable FDTD technique. In addition, parallel cyclic reduction is adapted to hepta-diagonal systems, and it is proven that GPU parallelization can offer non-trivial benefits to implicit FDTD approaches as well.

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“…In this communication, we present further reinterpretation of multi-stage implicit FDTD schemes in [8]. In particular, the equivalence of several multi-stage SS schemes will be shown based on amplification matrices and power property of eigenvalues in dispersion relations.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, various multi-stage split-step (SS) finitedifference time-domain (FDTD) schemes [1]- [6] have been proposed which may feature better performances such as higher accuracy, lower anisotropy, etc compared to the conventional two-stage SS [or locally-one-dimensional (LOD)] scheme [7]. In [8], it was shown that certain four-stage SS schemes [3], [5], [6] can be reinterpreted as two-stage ones [7], [9] with different time step scaling. The explicit expressions for dispersion relations and truncation error matrices were provided for these schemes in 2D to show the equivalence.…”

Section: Introductionmentioning

confidence: 99%

Further Reinterpretation of Multi-Stage Implicit FDTD Schemes

Heh

Tan

2014

IEEE Trans. Antennas Propagat.

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This communication presents further reinterpretation of multi-stage implicit finite-difference time-domain (FDTD) schemes. The equivalence of several multi-stage split-step (SS) schemes is shown based on amplification matrices and power property of eigenvalues in dispersion relations. In doing so, the explicit expressions for dispersion relations need not be derived, thus amenable to 3D and generalized multi-stage SS schemes conveniently. The improvement of temporal accuracy for generalized multi-stage SS schemes using generalized input and output processing matrices is also provided. It is further shown that the SS, alternating-direction-implicit (ADI) as well as the recently proposed divergence-preserving (DP) ADI schemes can be interpreted based on the more concise matrix exponential.

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Reinterpreting Four-Stage Split-Step FDTD Methods as Two-Stage Methods

Cited by 5 publications

References 13 publications

Accuracy Limitations of the Locally One-Dimensional FDTD Technique

Accuracy Limitations of the Locally One-Dimensional FDTD Technique

Accelerated unconditionally stable FDTD scheme with modified operators

Further Reinterpretation of Multi-Stage Implicit FDTD Schemes

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