A review of hybrid implicit explicit finite difference time domain method

Chen, Juan

doi:10.1016/j.jcp.2018.02.053

Cited by 21 publications

(12 citation statements)

References 89 publications

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“…Whereas, the HIE-FDTD method only executes implicit difference schemes for the spatial partial derivatives in the direction along which there are fine structures and takes general explicit difference schemes for the remaining spatial partial derivatives in the directions along which there are no fine elements. In such an arrangement, the HIE-FDTD method finishes the restriction of the fine spatial cell sizes on time step size, acquires the ability to improve computational efficiency, and has drawn much attention in recent years [19][20][21][22]. Compared with the conventional FDTD method and even some other absolutely stable FDTD methods such as the ADI-FDTD method in some situations [23], the HIE-FDTD method showed higher efficiency, and a lot of work including but not limited to simulations of designing devices, implementations of PML, and reducing numerical dispersion error [19][20][21][22]24] have been put forward.…”

Section: Introductionmentioning

confidence: 99%

A Memory-Efficient Hybrid Implicit–Explicit FDTD Method for Electromagnetic Simulation

Chen

2022

ACES Journal

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As the explicit finite-difference time-domain (FDTD) method is restricted by the Courant−-Friedrich−-Levy (CFL) stability condition and inefficient for simulation in some situations, implicit methods are developed. The hybrid implicit−-explicit (HIE) FDTD method is one popular method among them. In this paper, a memory-efficient HIE FDTD method is designed for electromagnetic simulation. The proposed HIE-FDTD method is based upon the divergence relationship of electric fields, nearly reduces one field component, and realizes a memory reduction rate of 33% approximately. Two numerical experiments are carried out to validate the proposed method and the results indicate that the proposed memory-efficient HIE-FDTD method can work well.

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Section: Introductionmentioning

confidence: 99%

A Memory-Efficient Hybrid Implicit–Explicit FDTD Method for Electromagnetic Simulation

Chen

2022

ACES Journal

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“…In order to overcome the CFL stability condition and improve computational efficiency, various implicit difference schemes have been adopted. Many implicit FDTD methods have been proposed, and all those methods show valuable performance improvement, such as hybrid implicit-explicit (HIE) FDTD method [3,4], Crank-Nicolson (CN) FDTD method [5,6], alternating-direction-implicit (ADI) FDTD method [7,8], locally-one-dimensional (LOD) FDTD method [9,10], and Weighted Laguerre Polynomial (WLP) FDTD method [11,12]. Among the implicit methods mentioned above, the HIE-FDTD method only applies implicit scheme to the spatial derivative in the direction along which there are fine elements, while taking general explicit scheme for the other spatial derivatives in the directions along which there are no fine structures.…”

Section: Introductionmentioning

confidence: 99%

One-Step Absolutely Stable FDTD Methods for Electromagnetic Simulation

Chen¹,

Li²

2021

PIER Letters

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As the explicit finite-difference time-domain (FDTD) method is restricted by the wellknown Courant-Friedruchs-Lewy (CFL) stability condition and is inefficient for solving numerical tasks with fine structures, various implicit methods have been proposed to tackle the problem, while many of them adopt time-splitting schemes that generally need at least two sub-steps to finish update at a full time step, and the strategies used seem to be an unnatural habit of computation compared with the most widely-used one-step methods. The procedure of splitting time step also reduces computational efficiency and makes implementation of these algorithms complex. In the present paper, two novel one-step absolutely stable FDTD methods including one-step alternating-direction-implicit (ADI) and one-step locally-one-dimensional (LOD) methods are proposed. The two proposed methods are derived from the original ADI-FDTD method and LOD-FDTD method through some linear operations applied to the original methods and are algebraically equivalent to the original methods respectively, but they both avoid the appearance of intermediate fields and are one-step method just like the conventional FDTD method. Numerical experiments are carried out for validation of the two proposed methods, and from the numerical results it can be concluded that the proposed methods can solve equation correctly and are simpler than the original methods, and their computation efficiency is close to that of the existing one-step leapfrog ADI-FDTD method.

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“…To overcome this problem, the weakly‐conditionally‐stable finite difference time domain (WCS‐FDTD) method has been proposed, which weakens the Courant‐Firedrich Levy (CFL) stability condition. A relatively large time step is applied to the WCS‐FDTD, as a result, the computation efficiency is improved …”

Section: Introdutionmentioning

confidence: 99%

“…A relatively large time step is applied to the WCS-FDTD, as a result, the computation efficiency is improved. [11][12][13][14][15][16] However, the computational formulas of the WCS-FDTD method are relatively complex in comparison with the conventional FDTD method. So, the WCS-FDTD method needs more memory to accomplish the whole computation, in spite of its computational efficiency is improved.…”

Section: Introdutionmentioning

confidence: 99%

A novel hybrid algorithm based on FDTD and WCS‐FDTD methods

Mai

Chen

et al. 2020

Int J RF Microw Comput Aided Eng

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In this article, a hybrid algorithm based on traditional finite‐difference time‐domain (FDTD) and weakly conditionally stable finite‐difference time‐domain (WCS‐FDTD) algorithm is proposed. In this algorithm, the calculation domain is divided into fine‐grid region and coarse‐grid region. The traditional FDTD method is used to calculate the field value in the coarse‐grid region, while the WCS‐FDTD method is used in the fine‐grid region. The spatial interpolation scheme is applied to the interface of the coarse grid region and fine grid region to insure the stability and precision of the presented hybrid algorithm. As a result, a relatively large time step size, which is only determined by the spatial cell sizes in the coarse grid region, is applied to the entire calculation domain. This scheme yields a significant reduction both of computation time and memory requirement in comparison with the conventional FDTD method and WCS‐FDTD method, which are validated by using numerical results.

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A review of hybrid implicit explicit finite difference time domain method

Cited by 21 publications

References 89 publications

A Memory-Efficient Hybrid Implicit–Explicit FDTD Method for Electromagnetic Simulation

A Memory-Efficient Hybrid Implicit–Explicit FDTD Method for Electromagnetic Simulation

One-Step Absolutely Stable FDTD Methods for Electromagnetic Simulation

A novel hybrid algorithm based on FDTD and WCS‐FDTD methods

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