Application of CUDA technology to calculation of ground states of few-body nuclei by Feynman's continual integrals method

Mikhail A. Naumenko; Vyacheslav V. Samarin

doi:10.14529/jsfi160206

Authors

Mikhail A. Naumenko The Joint Institute for Nuclear Research, Dubna
Vyacheslav V. Samarin The Joint Institute for Nuclear Research, Dubna

DOI:

https://doi.org/10.14529/jsfi160206

Abstract

The possibility of application of modern parallel computing solutions to speed up the calculations of ground states of few-body nuclei by Feynman's continual integrals method has been investigated. These calculations may sometimes require large computational time, particularly in the case of systems with many degrees of freedom. This paper presents the results of application of general-purpose computing on graphics processing units (GPGPU). The energy and the square modulus of the wave function of the ground states of several few-body nuclei have been calculated using NVIDIA CUDA technology. The results show that the use of GPGPU significantly increases the speed of calculations.

References

Penionzhkevich Yu.E. Reactions Involving Loosely Bound Cluster Nuclei: Heavy Ions and New Technologies // Phys. Atom. Nucl. 2011. Vol. 74. P. 1615-1622.

Skobelev N.K., Penionzhkevich Yu.E., Voskoboinik E.I. et al. Fusion and Transfer Cross Sections of 3He Induced Reaction on Pt and Au in Energy Range 10-24.5 MeV // Phys. Part. Nucl. Lett. 2014. Vol. 11. P. 208-215.

Wu Y., Ishikawa S., Sasakawa T. Three-Nucleon Bound States: Detailed Calculations of 3H and 3He // Few-Body Systems. 1993. Vol. 15. P. 145-188.

Dzhibuti R.I., Shitikova K.V. Metod gipersfericheskikh funktsiy v atomnoy i yadernoy ﬁzike [Method of Hyperspherical Functions in Atomic and Nuclear Physics]. Moscow, Energoatomizdat, 1993. 269 P.

Kievsky A., Marcucci L.E., Rosati S. et al. High-Precision Calculation of the Triton Ground State Within the Hyperspherical-Harmonics Method // Few-Body Systems. 1997. Vol. 22. P. 1-10.

Viviani M., Kievsky A., Rosati S. Calculation of the α-Particle Ground State // Few-Body Systems. 1995. Vol. 18. P. 25-39.

Voronchev V.T., Krasnopolsky V.M., Kukulin V.I. A Variational Study of the Ground and Excited States of Light Nuclei in a Three-body Model on the Complete Basis. I. General Formalism // J. Phys. G. 1982. Vol. 8. P. 649-666.

Feynman R.P., Hibbs A.R. Quantum Mechanics and Path Integrals. New York, McGrawHill, 1965. 382 P.

Blokhintsev D.I. Osnovy kvantovoy mekhaniki [Principles of Quantum Mechanics]. Moscow, Nauka, 1976. 608 P.

Shuryak E.V., Zhirov O.V. Testing Monte Carlo Methods for Path Integrals in Some Quantum Mechanical Problems // Nucl. Phys. B. 1984. Vol. 242. P. 393-406.

Shuryak E.V. Stochastic Trajectory Generation by Computer // Sov. Phys. Usp. 1984. Vol. 27. P. 448-453.

Lobanov Yu.Yu. Functional Integrals for Nuclear Many-particle Systems // J. Phys. A: Math. Gen. 1996. Vol. 29. P. 6653-6669.

L¨ahde T.A., Epelbaum E., Krebs H. et al. Lattice Eﬀective Field Theory for Medium-Mass Nuclei // Phys. Lett. B. 2014. Vol. 732. P. 110-115.

Borasoy B., Epelbaum E., Krebs H. et al. Lattice Simulations for Light Nuclei: Chiral Eﬀective Field Theory at Leading Order // Eur. Phys. J. A. 2007. Vol. 31. 105-123.

Samarin V.V., Naumenko M.A. Study of Ground States of 3,4,6He Nuclides by Feynman’s Continual Integrals Method // Bull. Russ. Acad. Sci. Phys. 2016. Vol. 80, No. 3. P. 283-289.

NVIDIA CUDA. URL: http://developer.nvidia.com/cuda-zone/ (accessed: 23.06.2016).

Sanders J., Kandrot E. CUDA by Example: An Introduction to General-Purpose GPU Programming. New York, Addison-Wesley, 2011. 290 P.

Perepyelkin E.E., Sadovnikov B.I., Inozemtseva N.G. Vychisleniya na graﬁcheskikh protsessorakh (GPU) v zadachakh matematicheskoy i teoreticheskoy ﬁziki [Computing on Graphics Processors (GPU) in Mathematical and Theoretical Physics]. Moscow, LENAND, 2014. 176 P.

Ermakov S.M. Metod Monte-Karlo v vychislitel’noy matematike: vvodnyy kurs [Monte Carlo Method in Computational Mathematics. Introductory Course]. St. Petersburg, Nevskiy Dialekt, 2009. 192 P.

Pollyak Yu.G. Veroyatnostnoe modelirovanie na elektronnykh vychislitel’nykh mashinakh [Probabilistic Modeling on Electronic Computers]. Moscow, Sovetskoe Radio, 1971. 400 P.

Satcher G.R., Love W.G. Folding Model Potentials from Realistic Interaction for Heavy-Ion Scattering // Phys. Rep. 1979. Vol. 55, No. 3. P. 185-254.

Alvarez M.A.G., Chamon L.C., Pereira D. et al. Experimental Determination of the Ion-Ion Potential in the N=50 Target Region: A Tool to Probe Ground-State Nuclear Densities // Nucl. Phys. A. 1999. Vol. 656, No. 2. P. 187-208.

NRV Web Knowledge Base on Low-Energy Nuclear Physics. URL: http://nrv.jinr.ru/ (accessed: 23.06.2016).

Heterogeneous Cluster of LIT, JINR. URL: http://hybrilit.jinr.ru/ (accessed: 23.06.2016).