GPU acceleration of Runge Kutta-Fehlberg and its comparison with Dormand-Prince method

Wo, Mei Seen; Gobithaasan, R. U.; Miura, Kenjiro T.

doi:10.1063/1.4887558

Cited by 9 publications

(8 citation statements)

References 3 publications

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“…The number of operations of this model is in the order of , meaning that when comparing 50 and 100 age categories, the latter has 4 times as many operations. As noted by previous work [ 21 – 23 ], small-scale ODE integration cannot fully utilize the GPU. By increasing the amount of age categories, the number of ODE equations grows proportionally and allows more GPU threads to be effectively used.…”

Section: Resultsmentioning

confidence: 99%

“…Amidst a plethora of numerical integration algorithms, Runge-Kutta methods are a family of implicit and explicit iterative methods, with a wide variety of orders and schemes [ 20 ]. Seen et al [ 21 ] implemented a Runge-Kutta-Fehlberg (commonly denoted RK45 ) with adaptive step size on an NVIDIA GPU. The authors demonstrated that the GPU outperforms a CPU implementation, given that the problem dimensions are large enough, as in 200 equations, or more.…”

Section: Related Workmentioning

confidence: 99%

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Heterogeneous computing for epidemiological model fitting and simulation

et al. 2018

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BackgroundOver the last years, substantial effort has been put into enhancing our arsenal in fighting epidemics from both technological and theoretical perspectives with scientists from different fields teaming up for rapid assessment of potentially urgent situations. This paper focusses on the computational aspects of infectious disease models and applies commonly available graphics processing units (GPUs) for the simulation of these models. However, fully utilizing the resources of both CPUs and GPUs requires a carefully balanced heterogeneous approach.ResultsThe contribution of this paper is twofold. First, an efficient GPU implementation for evaluating a small-scale ODE model; here, the basic S(usceptible)-I(nfected)-R(ecovered) model, is discussed. Second, an asynchronous particle swarm optimization (PSO) implementation is proposed where batches of particles are sent asynchronously from the host (CPU) to the GPU for evaluation. The ultimate goal is to infer model parameters that enable the model to correctly describe observed data. The particles of the PSO algorithm are candidate parameters of the model; finding the right one is a matter of optimizing the likelihood function which quantifies how well the model describes the observed data. By employing a heterogeneous approach, in which both CPU and GPU are kept busy with useful work, speedups of 10 to 12 times can be achieved on a moderate machine with a high-end consumer GPU as compared to a high-end system with 32 CPU cores.ConclusionsUtilizing GPUs for parameter inference can bring considerable increases in performance using average host systems with high-end consumer GPUs. Future studies should evaluate the benefit of using newer CPU and GPU architectures as well as applying this method to more complex epidemiological scenarios.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Heterogeneous computing for epidemiological model fitting and simulation

et al. 2018

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“…There are many numerical methods for CUDA to solve ODE. This article uses the most common Runge-Kutta-Merson method, interested can refer to [44][45][46][47].…”

Section: Using Matlab/cuda To Accelerate the Best Solutionmentioning

confidence: 99%

Study on Consulting Air Combat Simulation of Cluster UAV Based on Mixed Parallel Computing Framework of Graphics Processing Unit

Kung¹

2018

Electronics

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This paper combines matrix game theory with negotiating theory and uses U-solution to study the framework of the consulting air combat of UAV cluster. The processes to determine the optimal strategy in this paper follow three points: first, the UAV cluster are grouped into fleets; second, the best paring for the joint operations of the fleet member with the enemy fleet members are calculated; thirdly, consultations within the fleet are conducted to discuss the problems of optimal tactic, roles of main/assistance, and situational assessment within the fleet. In order to improve the computing efficiency of the framework, this article explores the use of the NVIDIA graphics processor programmed through MATLAB mixed C++/CUDA toolkit to accelerate the calculations of equations of motion of unmanned aerial vehicles, the prediction of superiority values and U values, computations of consultation, the evaluation of situational assessment and the optimal strategies. The effectiveness evaluation of GPGPU and CPU can be observed by the simulation results. When the number of team air combat is small, the CPU alone has better efficiency; however, when the number of air combat clusters exceeds 6 to 6, the architecture presented in this article can provide higher performance improvements and run faster than optimized CPU-only code.

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“…Methods like Runge-Kutta are multi-steps iterated methods [16][17][18][19]; this means one can distribute calculations of each step on different computing nodes. But at the end of each step, the different computing nodes should send their results to one node to sum-up or combine them appropriately and then calculate a new value.…”

Section: Introductionmentioning

confidence: 99%

Contribution to Speeding-Up the Solving of Nonlinear Ordinary Differential Equations on Parallel/Multi-Core Platforms for Sensing Systems

Tavakkoli

Mohsenzadegan

Chedjou

et al. 2020

Sensors

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Solving ordinary differential equations (ODE) on heterogenous or multi-core/parallel embedded systems does significantly increase the operational capacity of many sensing systems in view of processing tasks such as self-calibration, model-based measurement and self-diagnostics. The main challenge is usually related to the complexity of the processing task at hand which costs/requires too much processing power, which may not be available, to ensure a real-time processing. Therefore, a distributed solving involving multiple cores or nodes is a good/precious option. Also, speeding-up the processing does also result in significant energy consumption or sensor nodes involved. There exist several methods for solving differential equations on single processors. But most of them are not suitable for an implementation on parallel (i.e., multi-core) systems due to the increasing communication related network delays between computing nodes, which become a main and serious bottleneck to solve such problems in a parallel computing context. Most of the problems faced relate to the very nature of differential equations. Normally, one should first complete calculations of a previous step in order to use it in the next/following step. Hereby, it appears also that increasing performance (e.g., through increasing step sizes) may possibly result in decreasing the accuracy of calculations on parallel/multi-core systems like GPUs. In this paper, we do create a new adaptive algorithm based on the Adams–Moulton and Parareal method (we call it PAMCL) and we do compare this novel method with other most relevant implementations/schemes such as the so-called DOPRI5, PAM, etc. Our algorithm (PAMCL) is showing very good performance (i.e., speed-up) while compared to related competing algorithms, while thereby ensuring a reasonable accuracy. For a better usage of computing units/resources, the OpenCL platform is selected and ODE solver algorithms are optimized to work on both GPUs and CPUs. This platform does ensure/enable a high flexibility in the use of heterogeneous computing resources and does result in a very efficient utilization of available resources when compared to other comparable/competing algorithm/schemes implementations.

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GPU acceleration of Runge Kutta-Fehlberg and its comparison with Dormand-Prince method

Cited by 9 publications

References 3 publications

Heterogeneous computing for epidemiological model fitting and simulation

Heterogeneous computing for epidemiological model fitting and simulation

Study on Consulting Air Combat Simulation of Cluster UAV Based on Mixed Parallel Computing Framework of Graphics Processing Unit

Contribution to Speeding-Up the Solving of Nonlinear Ordinary Differential Equations on Parallel/Multi-Core Platforms for Sensing Systems

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