A Dissipation Theory for Three-Dimensional FDTD With Application to Stability Analysis and Subgridding

Bekmambetova, Fadime; Zhang, Xinyue; Triverio, Piero

doi:10.1109/tap.2018.2869617

Cited by 19 publications

(8 citation statements)

References 24 publications

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“…The time step 4.6701 ps is used in all the simulations for fair comparison. According to [22], the SAR is given by absolute value of the electric field component, the specific conductance and density of the corresponding structure.…”

Section: B the Sar Calculationmentioning

confidence: 99%

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A SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components

Wang¹,

Yu²,

Wang³

et al. 2022

Preprint

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A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method is proposed to model geometrically fine structures in this paper. Compared with our previous work, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or modifying any field components through field extrapolation on the boundaries to make the discrete operators satisfy the SBP property. The accuracy of extrapolation keeps consistency with that of the second-order finite-difference scheme near the boundaries. In addition, the SATs are used to weakly enforce the tangential boundary conditions between multiple mesh blocks with different mesh sizes. With carefully designed interpolation matrices and selected free parameters of the SATs, no dissipation occurs in the whole computational domain. Therefore, its long-time stability is theoretically guaranteed. Three numerical examples are carried out to validate its effectiveness. Results show that the proposed SBP-SAT FDTD subgridding method is stable, accurate, efficient, and easy to implement based on existing FDTD codes with only a few modifications.

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Section: B the Sar Calculationmentioning

confidence: 99%

“…Furthermore, another two symmetric and stable subgridding algorithms were proposed in [20], [21]. Recently, a dissipation theory was proposed to prove the stability of the FDTD methods with applications to subgridding algorithms [22], [23] in two-and three-dimensional space.…”

mentioning

confidence: 99%

A SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components

Wang¹,

Yu²,

Wang³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…An asymmetric FDTD subgridding technique was proposed in [17], which can be used for any mesh refinement ratio. It's well-known that the long-time stability of those subgridding algorithms can not be always guaranteed since the theoretical proofs can hardly be given through making interpolation operators meet the reciprocity principle [18] or the dissipation theory [19].…”

Section: Introductionmentioning

confidence: 99%

Towards the Development of A Three-Dimensional SBP-SAT FDTD Method: Theory and Validation

Yu¹,

Liu²,

Wang³

et al. 2022

Preprint

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To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex electromagnetic problems. It is theoretically stable and can be further used for multiple mesh blocks with different mesh sizes. This paper mainly focuses on the fundamental theoretical aspects upon its three-dimensional implementation, the SAT for various boundary conditions, and the numerical dispersion properties and the comparison with the FDTD method. The proposed SBP-SAT FDTD method inherits all the merits of the FDTD method, which is matrix-free, easy to implement, and has the same level of accuracy with a negligible overhead of runtime (0.13%) and memory usage (1.2%). Four numerical examples are carried out to validate the effectiveness of the proposed method.

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“…The current mainstream numerical algorithms (e.g. finite difference time-domain [8][9][10], finite element method [11], method of moments [12], discontinuous Galerkin time-domain (DGTD) [13][14][15][16][17][18][19][20] etc.) and commercial software (e.g.…”

Section: Introductionmentioning

confidence: 99%

Efficient electromagnetic analysis of multi‐layer and multi‐scale periodic/quasi‐periodic structures

Wen

Wang

2022

IET Microwaves Antenna & Prop

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To increase the electromagnetic analysis efficiency, the fast and memory efficient discontinuous Galerkin time‐domain (DGTD) method, which can simulate expeditiously the multi‐scale and multi‐layer periodic/quasi‐periodic structures, is proposed in this study. For one thing, this method is highly targeted for multi‐layer quasi‐periodic structures. It realises that the quasi‐periodic structure is extended from one layer to multiple layers. At the same time, the unit cells of the structure are no longer the conventional square lattice, and the sizes of different types of unit cells cannot be required for the same. For another, the implicit–explicit Runge–Kutta (ImEx‐RK) time stepping scheme has been widely employed for time integration, which can break the limitation of the Courant–Friedrichs–Levy condition. However, the ImEx‐RK time stepping scheme had been an under‐explored domain in periodic/quasi‐periodic structures, so it was introduced into the memory efficient DGTD method to decrease the simulation time. That is, the electrically coarse and fine subdomains in the multiscale periodic/quasi‐periodic structures can be separated such that implicit schemes can be utilised in the fine subdomains. The correctness and advance of this method are proved by several classical numerical examples.

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A Dissipation Theory for Three-Dimensional FDTD With Application to Stability Analysis and Subgridding

Cited by 19 publications

References 24 publications

A SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components

A SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components

Towards the Development of A Three-Dimensional SBP-SAT FDTD Method: Theory and Validation

Efficient electromagnetic analysis of multi‐layer and multi‐scale periodic/quasi‐periodic structures

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