Solving Poisson’s equation using FFT in a GPU cluster

Jodra, Jose Luis; Gurrutxaga, Ibai; Muguerza, Javier; Yera, Ainhoa

doi:10.1016/j.jpdc.2016.09.004

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…This study proposes the Triangular Wave Analysis (TWA) technology for traffic volume processing. Through the analyses of STE and MFCC characteristic traffic detection methods in [30], both methods have certain limitations in detecting the performance of overlapping congested segments. The indicator of STE (E i ) of the traffic noise signal is calculated by taking d 0 m (i, n) from d m (i, n) in MFCC, and the first and last two frames of the short-time energy E i of the traffic noise signal are discarded because the frames were not included in calculating d m (i, n).…”

Section: Traffic Detection Based On Triangle Wave Analysis Of Traffic...mentioning

confidence: 99%

A Novel Driving Noise Analysis Method for On-Road Traffic Detection

Liu

et al. 2022

Sensors

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Effective noise reduction and abnormal feature extraction are important for abnormal sound detection occurring in urban traffic operations. However, to improve the detection accuracy of continuous traffic flow and even overlapping vehicle bodies, effective methods capable to achieve accurate signal-to-noise ratio and appropriate characteristic parameters should be explored. In view of the disadvantages of traditional traffic detection methods, such as Short-Time Energy (STE) and Mel Frequency Cepstral Coefficients (MFCC), this study adopts an improved spectral subtraction method to analyze traffic noise. Through the feature fusion of STE and MFCC coefficients, an innovative feature parameter, E-MFCC, is obtained, assisting to propose a traffic noise detection solution based on Triangular Wave Analysis (TWA). APP Designer in MATLAB was used to establish a traffic detection simulation platform. The experimental results showed that compared with the accuracies of traffic detection using the traditional STE and MFCC methods as 67.77% and 76.01%, respectively, the detection accuracy of the proposed TWA is significantly improved, attaining 91%. The results demonstrated the effectiveness of the traffic detection method proposed in solving the overlapping problem, thus achieving accurate detection of road traffic volume and improving the efficiency of road operation.

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Section: Traffic Detection Based On Triangle Wave Analysis Of Traffic...mentioning

confidence: 99%

A Novel Driving Noise Analysis Method for On-Road Traffic Detection

Liu

et al. 2022

Sensors

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“…Workstations and data servers with multiple GPUs are now widely available, and it is imperative for modelling software to unlock the full potential of modern hardware. It should be noted that multi-GPU methods have been introduced in other fields, notably in computational electromagnetics where Poisson's equation is solved using fast Fourier transforms (FFT) with good scalability up to 16 GPUs [20], and multi-GPU parallelization of 3D FFTs was also discussed [21].…”

Section: Introductionmentioning

confidence: 99%

Accelerating micromagnetic and atomistic simulations using multiple GPUs

Lepadatu

2023

Journal of Applied Physics

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It is shown that micromagnetic and atomistic spin dynamics simulations can use multiple graphical processing units (GPUs) not only to reduce computation time but also to allow for a larger simulation size than is possible on a single GPU. While interactions that depend on neighboring spins, such as exchange interactions, may be implemented efficiently by transferring data between GPUs using halo regions or direct memory accesses, implementing the long-range demagnetizing interaction is the main difficulty in achieving good performance scaling, where the data transfer rate between GPUs is a significant bottleneck. A multi-GPU convolution algorithm is developed here, which relies on single-GPU FFTs executed in parallel. It is shown that even for micromagnetic simulations where the demagnetizing interaction computation time dominates, good performance scaling may be achieved, with speedup factors up to 1.8, 2.5, and 3.1, for two, three, and four GPUs, respectively. The code developed here can be used for any number of GPUs in parallel, with performance scaling strongly dependent on the inter-GPU data transfer rate and connection topology. This is further improved in micromagnetic simulations, which include a spin transport solver, obtaining speedup factors up to 1.96, 2.8, and 3.7, for two, three, and four GPUs, respectively. The best case scenario is obtained for atomistic simulations, where the demagnetizing interaction is implemented with spin-averaged cells. Using a single workstation with four GPUs, it is shown that atomistic spin dynamics simulations with up to 1 × 109 spins and atomistic Monte Carlo simulations with up to 2 × 109 spins are possible, with near-ideal performance scaling.

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“…For the above mentioned solutions, the scalability of the algorithm was tested on Bluegene and Cray XT/XC architectures, for some up to 64k cores and more, often showing similar performances. Concurrently, hardware acceleration applied to Poisson's problem has also been considered [16].…”

Section: Introductionmentioning

confidence: 99%

FLUPS: a Fourier-based Library of Unbounded Poisson Solvers

Caprace,

Gillis,

Chatelain

2020

Preprint

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A Fourier-based Library of Unbounded Poisson Solvers (FLUPS) for 2-D and 3-D homogeneous distributed grids is presented. It is designed to handle every possible combination of periodic, symmetric, semi-unbounded and fully unbounded boundary conditions for the Poisson equation. FLUPS leverages a dedicated implementation of 3-D Fourier transforms to solve the Poisson equation using Green's functions, in a fast and memory-efficient way. Several Green's functions are available, optionally with explicit regularization or using Lattice Green Functions, and provide verified convergence orders from 2 to 6. The algorithm depends on the FFTW library to perform 1-D transforms, while MPI communications enable the required remapping of data in memory. For the latter operation, a first available implementation resorts to the standard all-to-all routines. A second implementation, featuring non-blocking and persistent pointto-point communications, is however shown to be more efficient in a majority of cases and especially while taking advantage of the shared memory parallelism with OpenMP. The scalability of the algorithm, aimed at massively parallel architectures, is demonstrated up to 73 720 cores. The results obtained with three different supercomputers show that the weak efficiency remains above 40% and the strong efficiency above 30% when the number of cores is multiplied by 16, for typical problems. These figures are slightly better than those expected from a third party 3-D FFT tool, with which a 20% longer execution time was also measured on average. From the outside, the solving procedure is fully automated so that the user benefits from the optimal performances while not having to handle the complexity associated with memory management, data mapping and Fourier transform computation. The parallel code is available under GPLv3 license at github.com/vortexlab-uclouvain/flups.

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Solving Poisson’s equation using FFT in a GPU cluster

Cited by 7 publications

References 25 publications

A Novel Driving Noise Analysis Method for On-Road Traffic Detection

A Novel Driving Noise Analysis Method for On-Road Traffic Detection

Accelerating micromagnetic and atomistic simulations using multiple GPUs

FLUPS: a Fourier-based Library of Unbounded Poisson Solvers

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