Long vectors algorithms for solving grid equations of explicit difference schemes
Vorotnikova D.G., Golovashkin D.L.


Image Processing Systems Institute, Russian Academy of Sciences,
Samara State Aerospace University


DOI: 10.18287/0134-2452-2015-39-1-87-93

Full text of article: Russian language.

We propose two variants of long vectors algorithms for solving grid equations of explicit difference schemes, allowing one to use the maximum number of CUDA cores even for a small dimension of the grid domain. The implementation of these algorithms is shown by the example of the heat conduction equation and the solution of Maxwell's equations. The comparison between the proposed algorithms implemented by means of the CUBLAS library and free software packages B-CALM and OpenCurrent is done.

heat equation, Maxwell’s equations, difference scheme, PDE, CUBLAS.


  1. The global forecast for the development of silicon technology [Electronical Resource]. – http://www.russianelectro­nics.ru/leader-r/review/doc/64629/ (request date 15.12.2014). – (In Russian).
  2. General-purpose computing on graphics processing units [Electronical Resource]. – http://www.gpgpu.org/ (request date 18.12.2014).
  3. Flynn, M.J. Very High-Speed Computing System / M.J. Flynn // Proceedings IEEE. – 1966. – Vol. 54(12). – P. 1901-1909.
  4. Ortega, J. Introduction to Parallel and Vector Solution of Linear Systems / J. Ortega. – New York: Plenum Press, 1987. – 313 p.
  5. GolubG.H. Matrix Computations / G.H. Golub, Ch.F. Van Loan. – JHU Press, 1996. – 747 p.
  6. Murray, C.M. The Supermen: The Story of Seymour Cray and the Technical Wizards Behind the Supercomputer / Ch.J. Murray. – Wiley, 1997. – 232 p.
  7. NVIDIA GeForce [Electronical Resource]. – http://www.nvi­dia.ru/object/geforce-family-ru.html (request date 18.12.2014).
  8. NVIDIA Tesla [Electronical Resource]. – http://www.nvi­dia.ru/object/tesla-high-performance-computing-ru.html (request date 16.12.2014).
  9. Samarski, A.A. Introduction into the theory of difference schems / A.A. Samarski. – Moscow: “Nayka” Publisher, 1971. – 552 p. – (In Russian).
  10. Volkov, K.N. Numerical solution of hydrodynamics problems by means of graphical processors / K.N. Volkov, V.N. Emelanov, A.G. Karpenko, I.V. Kyrova, A.E. Serov // Calculating methods and programming. – 2013. – Vol. 14(1). – P. 82-90. – (In Russian).
  11. OpenCurrent is an open source C++ library for solving Partial Differential Equations (PDEs) over regular grids using the CUDA platform from NVIDIA [Electronical Resource]. – https://code.google.com/p/opencurrent/ (request date 18.12.2014).
  12. Wahl, P. B-CALM: An open-source GPU-based 3D-FDTD with multi-pole dispersion for plasmonics / P. Wahl, D.-S. Ly-Gagnon, Ch. Debaes, D.A.B. Miller, H. Thienpont // Optical and Quantum Electronics. – 2012. – Vol. 44. – P. 285-290.
  13. Golovashkin, D.L. Solving finite-difference equations for diffractive optics problems using graphics processing units / D.L. Golovashkin, D. Vorotnikova, A. Kochurov, S. Maly­sheva // Optical Engineering. – 2013. – Vol. 52(9). – Doi: 10.1117/1.OE.52.9.091719.
  14. Golovashkin, D.L. Solution of difference equations in graphical computing devices. Method of pyramids / D.L. Golovashkin, A.V. Kochurov // Computing Technologies. – 2012. – Vol. 17(3). – P. 55-69. – (In Russian).
  15. Diffractive nanophotonics / A.V. Gavrilov, D.L. Golovashkin, , L.L. Doskolovich, P.N. Dyachenko, A.A. Kovalev, V.V. Kot­lyar, A.G. Nalimov, D.V. Nesterenko, V.S. Pavelyev, R.V. Ski­danov, V.A. Soifer, S.N. Khonina, Ya.O. Shuyupova. – Ed. by V.A. Soifer. – Moscow, “Fizmatlit” Publisher, 2011. – 680 p. – (In Russian).

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