A Stable 3-D FDTD Method with Multiple Embedded Reduced-Order Models

Zhang, Xinyue; Triverio, Piero

doi:10.1109/apusncursinrsm.2019.8888640

Cited by 2 publications

(4 citation statements)

References 7 publications

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“…It can be seen that the partial derivative of electromagnetic fields with respect to time can be replaced by (7a)-( 7c) and ( 9)- (11). Therefore, we can obtain dE/dt by substituting (7a)-( 7c) and ( 9)-( 11) into (15). After some mathematical manipulations, ( 15) can be expressed as…”

Section: A Proposed Sbp-sat Fdtd Methods With the Pec Boundary Conditionmentioning

confidence: 99%

“…After taking the derivative of electromagnetic energy in the computational domain with respect to time, dE/dt can be expressed by the derivative of electromagnetic fields. By substituting (7d)-(7f) and ( 18)-( 20) into (15), dE/dt can be written as…”

Section: B Proposed Sbp-sat Fdtd Methods With the Pmc Boundary Conditionmentioning

confidence: 99%

“…However, it may be computationally expensive for large-scale problems to calculate those stable modes in simulations. In [14] and [15], a reduced-order model (MOR) was used in the subgridding scheme to extend the Courant-Friedrichs-Lewy (CFL) condition for improving the efficiency. Another high-order smoothing technique was proposed to interpolate fields on the interfaces in the nonstandard (NS)-FDTD method [16].…”

mentioning

confidence: 99%

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Toward the Development of a 3-D SBP-SAT FDTD Method: Theory and Validation

Cheng

Liu

Wang

et al. 2023

IEEE Trans. Antennas Propagat.

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To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a 3-D summation-by-part 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 article mainly focuses on the fundamental theoretical aspects upon its 3-D 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 matrixfree, easy to implement, and has the same level of accuracy with a negligible overhead of runtime and memory usage. Four numerical examples are carried out to validate the effectiveness of the proposed method.

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Section: A Proposed Sbp-sat Fdtd Methods With the Pec Boundary Conditionmentioning

confidence: 99%

Section: B Proposed Sbp-sat Fdtd Methods With the Pmc Boundary Conditionmentioning

confidence: 99%

mentioning

confidence: 99%

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Toward the Development of a 3-D SBP-SAT FDTD Method: Theory and Validation

Cheng

Liu

Wang

et al. 2023

IEEE Trans. Antennas Propagat.

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show abstract

“…However, it may be computationally expensive for large-scale problems to calculate those stable modes in simulations. In [14] [15], a reduced-order model (MOR) was used in the subgridding scheme to extend the Courant-Friedrichs-Lewy (CFL) condition for improving the efficiency. Another highorder smoothing technique was proposed to interpolate fields on the interfaces in the non-standard (NS)-FDTD method [16].…”

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.

show abstract

A Stable 3-D FDTD Method with Multiple Embedded Reduced-Order Models

Cited by 2 publications

References 7 publications

Toward the Development of a 3-D SBP-SAT FDTD Method: Theory and Validation

Toward the Development of a 3-D SBP-SAT FDTD Method: Theory and Validation

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

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