Implementation of Beeman's algorithm to calculate execution time on GPU using CUDA




Beeman algorithm, GPU, CPU, Thread, Bloc, Grille, CUDA C/C


Graphics processing units (GPUs) are microprocessors designed to the operation of display and manipulation of graphics data. . Currently, these graphics processor are found on all graphics hardware and have become very important instruments for parallel computing. GPUs are practical tools for the development of several fields like decoding and encoding, solving differential equations. Their advantages are increase in performance, faster data processing and reduced power consumption. It is simple to program a GPU with CUDA C to run parallel calculations. But it is necessary to have an understanding of the architectural aspects of the GPU and CUDA C. This paper, we will describe and implement Beeman's algorithm on GPU and CPU using CUDA C to solve the differential equation of charged particles in an electromagnetic field. Our goal is to evaluate the performances of the implementation on GPU and CPU processors and to deduce the efficiency of the use of GPUs.


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Beeman, David. "Some multistep methods for use in molecular dynamics calculations", Journal of Computational Physics, vol. 20, no. 2, pp. 130–139, 1976.

Schofield, P. "Computer simulation studies of the liquid state", Computer Physics Communications, 5 (1): 17–23, 1973. DOI:

Levitt, Michael; Meirovitch, Hagai; Huber, R. "Integrating the equations of motion", Journal of Molecular Biology, 168 (3): 617–620, 1983. DOI:

NVIDIA. "NVIDIA CUDA Compute Unified Device Architecture Programming Guide," Version 2.0, 2008.

WD Sproul. "Surface and Coatings Technology," 1996, Elsevier.

Manish Arora. “The Architecture and Evolution of CPU- GPU Systems for General Purpose-Computing, “2012.

Yadav K., Mittal A., Ansari M. A., Vishwarup V. “Parallel Implementation of Similarity Measures on GPU Architecture using CUDA,” 2012.

Jayshree Ghorpade, Jitendra Parande, Madhura Kulkarni, Amit Bawaskar. “GPGPU PROCESSING IN CUDA

ARCHITECTURE,” Advanced Computing: An International Journal (ACIJ), Vol.3, No.1, January 2012.

D. Beeman, J Camp. Phys, pp. 20-130, 1976. DOI:

D. Beeman, J Camp. Phys, pp. 52- 24, 1983. DOI:

C. W. Gear. "Numerical initial value problems in ordinary differential equations", Newyork, Prentice-Hall,1971.

I.A. Mc Cammon and M. Karplus, Nature, pp. 268-765, 1977. DOI:

I.A. Mc Cammon and M. Karplus, Proc. Nat. Acad Sei. USA, pp.58, 1979.

NVIDIA. Whitepaper NVIDIA’s next Generation CUDA Compute Architecture. Nvidia Corp, p. 21, 2009.




How to Cite

Y. Rtal and A. Hadjoudja, “Implementation of Beeman’s algorithm to calculate execution time on GPU using CUDA”, EAI Endorsed Trans IoT, vol. 8, no. 4, p. e4, Dec. 2022.