A 3D hybrid implicit‐explicit FDTD scheme with weakly conditional stability

Abstract-The conventional Finite-Difference Time-Domain (FDTD) method with staggered Yee scheme does not easily allow including thin material layers, especially so if these layers are highly conductive. This paper proposes a novel subgridding technique for 2D problems, based on a Hybrid Implicit-Explicit (HIE) scheme, that efficiently copes with this problem. In the subgrid, the new method collocates field components such that the thin layer boundaries are defined unambiguously. Moreover, aspect ratios of more than a million do not impair the stability of the method and allow for very accurate predictions of the skin effect. The new method retains the Courant limit of the coarse Yee grid and is easily incorporated into existing FDTD codes. A number of illustrative examples, including scattering by a metal grating, demonstrate the accuracy and stability of the new method.

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“…The upper and lower interface conditions are readily retrieved by testing Ampère's law (2) with the HIE testing function (21). Fig.…”

Section: Interface Conditionmentioning

confidence: 99%

“…Besides these purely implicit methods, whether or not combined with conventional FDTD in a multigrid configuration, another kind of (partially) implicit schemes exist: the so-called Hybrid Implicit-Explicit (HIE) FDTD methods [21,22]. They are used to analyse structures that are fine in at least one but not all directions.…”

Section: Introductionmentioning

confidence: 99%

A New Hybrid Implicit–Explicit FDTD Method for Local Subgridding in Multiscale 2-D TE Scattering Problems

Londersele

Zutter

Ginste

2016

IEEE Trans. Antennas Propagat.

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“…Meanwhile, in the ADI-SFDTD method, four untridiagonal matrices, two tridiagonal matrices, and six explicit equations should be solved in one update cycle, which makes it computationally inefficient. To overcome the drawbacks of the ADI-FDTD, recently, a hybrid implicit-explicit (HIE) FDTD method was submitted [29,30], the computation complexity of the HIE-FDTD method is the same as that of the conventional FDTD method, while the CFL condition restraint is weaker than that of the conventional FDTD method and consequently, less CPU time is required. This advantage can be more obvious when fine structures are involved.…”

Section: Introductionmentioning

confidence: 99%

“…The time step in this method is only determined by two space discretizations [30]. To eliminate the time delay in transverse plane, the CTW wave [27] is applied, as a result, the FDTD code needs to be changed from real variables to complex variables, which is different from conventional HIE-FDTD method.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

Mao¹,

Chen²,

Liu³

et al. 2012

PIER

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Abstract-This paper combines a hybrid implicit-explicit (HIE) method with spectral finite-difference time-domain (SFDTD) method for solving periodic structures at oblique incidence, resulting in a HIE-SFDTD method. The new method has the advantages of both HIE-FDTD and SFDTD methods, not only making the stability condition weaker, but also solving the oblique incident wave on periodic structures. Because the stability condition is determined only by two space discretizations in this method, it is extremely useful for periodic problems with very fine structures in one direction. The method replaces the conventional single-angle incident wave with a constant transverse wave-number (CTW) wave, so the fields have no delay in the transverse plane, as a result, the periodic boundary condition (PBC) can be implemented easily for both normal and oblique incident waves. Compared with the ADI-SFDTD method it only needs to solve two untridiagonal matrices when the PBC is applied to, other four equations can be updated directly, while four untridiagonal matrices, two tridiagonal matrices, and six explicit equations should be solved in the ADI-SFDTD method. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed algorithm. Results show the new algorithm has better accuracy and higher efficiency than that of the ADI-SFDTD method, especially for large time step sizes. The CPU running time for this method can be reduced to about 45% of the ADI-SFDTD method.

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“…To relax the Courant limit on the time step size of the FDTD method, a three-dimensional (3-D) hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method has been developed recently [3]. In this method, the CFL condition is not removed totally, but being weaker than that of the conventional FDTD method.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Method to Reduce the Numerical Dispersion in the HIE-FDTD Scheme

Chen¹,

Zhang²

2011

WET

Self Cite

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A 3D hybrid implicit‐explicit FDTD scheme with weakly conditional stability

Abstract: Ϫϱ t ABSTRACT: In this paper, the hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) algorithm for a two-dimensional (2D) TE wave is extended to a full three-dimensional (3D) wave. The weakly conditional stability is verified by numerical simulation results. Numeri-

Cited by 83 publications

References 3 publications

A New Hybrid Implicit–Explicit FDTD Method for Local Subgridding in Multiscale 2-D TE Scattering Problems

A New Hybrid Implicit–Explicit FDTD Method for Local Subgridding in Multiscale 2-D TE Scattering Problems

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

An Efficient Method to Reduce the Numerical Dispersion in the HIE-FDTD Scheme

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