An Efficient Domain Decomposition Parallel Scheme for Leapfrog ADI-FDTD Method

Bao, Huaguang; Chen, R. S.

doi:10.1109/tap.2016.2647587

Cited by 31 publications

(6 citation statements)

References 29 publications

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“…To accelerate the numerical solution of the discretized Maxwell equations, domain decomposition parallelization schemes have been studied, aiming at partitioning the computational domain into several subdomains [24], [25]. The solution of the update equations at each subdomain is allocated to a different processing unit and subsequently, the individual solutions are combined to derive a solution for the entire domain.…”

Section: Related Workmentioning

confidence: 99%

Stochastic Evaluation of Indoor Wireless Network Performance with Data-Driven Propagation Models

Bakirtzis

Wassell

Fiore

et al. 2022

GLOBECOM 2022 - 2022 IEEE Global Communications Conference

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Computational electromagnetics (CEM) is employed to numerically solve Maxwell's equations, and it has very important and practical applications across a broad range of disciplines, including biomedical engineering, nanophotonics, wireless communications, and electrodynamics. The main limitation of existing CEM methods is that they are computationally demanding. Our work introduces a leap forward in scientific computing and CEM by proposing an original solution of Maxwell's equations that is grounded on graph neural networks (GNNs) and enables the high-performance numerical resolution of these fundamental mathematical expressions. Specifically, we demonstrate that the update equations derived by discretizing Maxwell's partial differential equations can be innately expressed as a two-layer GNN with static and pre-determined edge weights. Given this intuition, a straightforward way to numerically solve Maxwell's equations entails simple message passing between such a GNN's nodes, yielding a significant computational time gain, while preserving the same accuracy as conventional transient CEM methods. Ultimately, our work supports the efficient and precise emulation of electromagnetic wave propagation with GNNs, and more importantly, we anticipate that applying a similar treatment to systems of partial differential equations arising in other scientific disciplines, e.g., computational fluid dynamics, can benefit computational sciences.

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Section: Related Workmentioning

confidence: 99%

Stochastic Evaluation of Indoor Wireless Network Performance with Data-Driven Propagation Models

Bakirtzis

Wassell

Fiore

et al. 2022

GLOBECOM 2022 - 2022 IEEE Global Communications Conference

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“…In this systematic study, the efficient direct-splitting-based CN-FDTD (CNDS-FDTD) method with the CFS-PML scheme is proposed based on the auxiliary differential equation (ADE) method to model 3D all-dielectric photonic nanostructures with monolayer BP metasurfaces in the infrared Terahertz range. The CFS-CNDS-FDTD not only possess higher efficiency than the alternating-direction-implicit FDTD (ADI-FDTD) method [43][44][45][46] due to owning fewer loops at each time step, but is suitable for parallel computation [47][48][49] which can be used to further reduce CPU time [39].…”

Section: Introductionmentioning

confidence: 99%

Direct-Splitting-Based CN-FDTD for Modeling 2D Material Nanostructure Problems

Feng

Zhang

Zeng

et al. 2020

IEEE Open J. Antennas Propag.

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Incorporating a truncation of the complex-frequencyshifted perfectly matched layer (CFS-PML), the direct-splittingbased Crank-Nicolson finite-difference time-domain (CNDS-FDTD) is developed and applied to the infrared two-dimensional layered material (2DLM) black phosphorous (BP) metasurface implementations on the all-dielectric nanostructure. To improve extremely low efficiencies in solving infrared terahertz (THz) problems with the few-atomic-layer thickness of 2DLMs, the CFS-CNDS-FDTD is proposed in demand due to the fact that it possesses capabilities of implicit FDTD method and unsplit-field CFS-PML truncation, respectively, in completely conquering the Courant-Friedrich-Levy condition (CFL) limit and holding good performance. The temporal incremental in the CFS-CNDS-FDTD can reach 1000 times larger than that in the regular FDTD for infrared nanoscale problems centered at the 2.5 THz and then keep accurate. Three-dimensional (3D) numerical cases have been carried out to corroborate the proposed method. The CFS-CNDS-FDTD can not only achieve high accuracies and then saves several dozen times of CPU time as compared to the regular FDTD, but also pave the way for designing all-dielectric nanostructures with other 2DLM metasurfaces. Index Terms-Black phosphorous (BP), Crank-Nicolson finitedifference time-domain (CN-FDTD), complex-frequency-shifted perfectly matched layer (CFS-PML), direct-splitting (DS), metasurface, two-dimensional layered material (2DLM).

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“…This was demonstrated in a number of studies that great efficiency gain of FDTD can be achieved through GPU acceleration. [16][17][18] Considerable research efforts have been devoted to multi-CPU based parallel implementations of unconditionallystable FDTD methods, namely, for ADI-FDTD, 19 for LOD-FDTD, 20 for leapfrog ADI-FDTD, 21 etc. However, these implementations cannot be simply extended to GPU environment because of the different hardware structure and execution models.…”

Section: Introductionmentioning

confidence: 99%

Implementation and optimization of GPU‐based parallel one‐step leapfrog ADI‐FDTD for far‐field scattering problems

Zou

Liu

Zhang

2020

Int J RF Microw Comput Aided Eng

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The one‐step leapfrog alternative‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD), free from the Courant‐Friedrichs‐Lewy (CFL) stability condition and sub‐step computations, is efficient when dealing with fine grid problems. However, solution of the numerous tridiagonal systems still imposes a great computational burden and makes the method hard to execute in parallel. In this paper, we proposed an efficient graphic processing unit (GPU)‐based parallel implementation of the one‐step leapfrog ADI‐FDTD for the far‐field EM scattering simulation of objects, in which we present and analyze the manners of calculation area division and thread allocation and a data layout transformation of z components is proposed to achieve better memory access mode, which is a key factor affecting GPU execution efficiency. The simulation experiment is carried out to verify the accuracy and efficiency of the GPU‐based implementation. The simulation results show that there is a good agreement between the proposed one‐step leapfrog ADI‐FDTD method and Yee's FDTD in solving the far‐field scattering problem and huge benefits in performance were encountered when the method was accelerated using GPU technology.

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An Efficient Domain Decomposition Parallel Scheme for Leapfrog ADI-FDTD Method

Cited by 31 publications

References 29 publications

Stochastic Evaluation of Indoor Wireless Network Performance with Data-Driven Propagation Models

Stochastic Evaluation of Indoor Wireless Network Performance with Data-Driven Propagation Models

Direct-Splitting-Based CN-FDTD for Modeling 2D Material Nanostructure Problems

Implementation and optimization of GPU‐based parallel one‐step leapfrog ADI‐FDTD for far‐field scattering problems

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