Development of the Three-Dimensional Unconditionally Stable LOD-FDTD Method

Ahmed, Iftikhar; Chua, Eng-Kee; Li, Er‐Ping; Chen, Zhizhang

doi:10.1109/tap.2008.2005544

Cited by 129 publications

(71 citation statements)

References 15 publications

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“…Some methods have been reported for ordinary FDTD based on implicit FDTD to overcome the Courant stability restraint on the time step of fully explicit FDTD. ADI-FDTD [13][14][15][16], and LOD-FDTD [17][18][19][20][21] have been developed for this purpose. In this way, up to 5 times reduction in computation times have been reported [21].…”

Section: Introductionmentioning

confidence: 99%

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Shahmansouri¹,

Rashidian²

2012

PIER

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Abstract-Split-field finite-difference time-domain (SF-FDTD) method can overcome the limitation of ordinary FDTD in analyzing periodic structures under oblique incidence. On the other hand, huge run times of 3D SF-FDTD, is practically a major burden in its usage for analysis and design of nanostructures, particularly when having dispersive media. Here, details of parallel implementation of 3D SF-FDTD method for dispersive media, combined with totalfield/scattered-field (TF/SF) method for injecting oblique plane wave, are discussed. Graphics processing unit (GPU) has been used for this purpose, and very large speed up factors have been achieved. Also a previously reported formulation of SF-FDTD based on the Drude model for dispersive media, is extended to cover Drude-Lorentz model, which is usually needed for materials such as gold. The resulting reduction in the number of variables in this formulation, not only helps in reducing the computational time, but also makes it possible to be implemented in GPU, where its memory limitation is a major concern. As an example for demonstrating the importance of this method in optimization of nanophotonics structures, improvement in the performance of a refractive index sensor, made of an array of nanodisks, using suitable angle of incidence is reported. To the best of our knowledge this is the first report of GPU implementation of SF-FDTD method, capable of analyzing periodic dispersive media under oblique incidence.

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Section: Introductionmentioning

confidence: 99%

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Shahmansouri¹,

Rashidian²

2012

PIER

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“…Along the same line, other unconditionally-stable methods such as split-step [37][38][39][40][41][42][43][44][45][46][47] and locally-one dimensional (LOD) [48][49][50][51][52] FDTD methods were developed. Specially, the two sub-steps method in [37], the three sub-steps methods in [38][39][40], the four sub-steps methods in [41][42][43][44] and six sub-steps methods in [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

“…The LOD-FDTD method can be considered as a split-step approach (SS1) with firstorder accuracy in time, which consumes less CPU time than that of the ADI-FDTD method. Particularly, The LOD-FDTD methods in 2-D [48,49], and 3-D LOD-FDTD methods with a three-step scheme [50] and a two-step scheme [51]. The method in [47] is based on the split-step scheme and Crank-Nicolson scheme, and denoted as SSCN6-FDTD herein.…”

Section: Introductionmentioning

confidence: 99%

Reduction of Numerical Dispersion of the Six-Stages Split-Step Unconditionally-Stable FDTD Method With Controlling Parameters

Kong¹,

Chu²

2012

PIER

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Abstract-A new approach to reduce the numerical dispersion of the six-stages split-step unconditionally-stable finite-difference timedomain (FDTD) method is presented, which is based on the splitstep scheme and Crank-Nicolson scheme. Firstly, based on the matrix elements related to spatial derivatives along the x, y, and z coordinate directions, the matrix derived from the classical Maxwell's equations is split into six sub-matrices. Simultaneously, three controlling parameters are introduced to decrease the numerical dispersion error. Accordingly, the time step is divided into six sub-steps. Secondly, the analysis shows that the proposed method is unconditionally stable. Moreover, the dispersion relation of the proposed method is carried out. Thirdly, the processes of determination of the controlling parameters are shown. Furthermore, the dispersion characteristics of the proposed method are also investigated, and the maximum dispersion error of the proposed method can be decreased significantly. Finally, numerical experiments are presented to substantiate the efficiency of the proposed method.

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“…Therefore, these equa tions are coupled t o simulate t hose a pplications in w hich c ombined effects are needed [12][13]. In [12] a hybrid transmission line matrix ( TLM) [14] and FDTD [15], and in [13] a hybr id locally one dimensional (LO D)-FDTD [16] and F DTD methods are applied to coupled non-dispersive Maxwell and Schrödinger equations. In [12] the FDTD method is app lied to Schrödinger eq uation to simu late ca rbon n anotube whil e the TL M metho d is applied to t he conventional n ondispersive Ma xwell e quations to simula te the r est of the structure.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrödinger Equations using the FDTD Method

Ahmed

2012

AEM

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A nume rical a pproach that cou ples Loren tz-Drude model incorporated Maxwell equations with Schrödinger equation is pre sented f or the simula tion of pla smonics na nodevices. Maxwell equa tions w ith Lore ntz-Drude (LD ) dispersive model are a pplied to l arge size c omponents, w hereas coupled Maxwell and Schrödinger equations are applied to components where quantum effec ts a re nee ded. The finite difference time do main me thod (F DTD) is appl ied to simulate these cou pled e quations. N umerical re sults of th e coupled ap proach are compared w ith th e conventional approach.

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Development of the Three-Dimensional Unconditionally Stable LOD-FDTD Method

Cited by 129 publications

References 15 publications

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Reduction of Numerical Dispersion of the Six-Stages Split-Step Unconditionally-Stable FDTD Method With Controlling Parameters

Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrödinger Equations using the FDTD Method

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