Solution of difference equations difference scheme with cyclic boundary conditions on two-dimensional grid areas using multiple graphics computing devices
D.L. Golovashkin, L.V. Loganova

Full text of article: Russian language.

Abstract:
The algorithms using cyclic sweep using CUDA technology to implement in one and two graphical computing devices. Of computational experiments have demonstrated the effectiveness of the approach.

Key words:
CUDA, parallel algorithms, tridiagonal systems.

References:

  1. Taflove, A. Computational Electrodynamics: The Finite-Difference Time-Domain Method / A. Taflove, S. Hag­ness. 3-nd. ed. – Boston: Arthech House Publishers, 2005. – 852 p.
  2. Inan, U.S. Numerical Electromagnetics: The FDTD Me­thod / Umran S. Inan, Robert A. Marshall. – New York: Cambridge University Press, 2011. – 390 p.
  3. Rouf, H.K. Implicit Finite Difference Time Domain Methods. Theory and Applications / Hasan Khaled Rouf. – LAP Lambert Academic, 2011. – 208 p.
  4. Gavrilov, A.V. The modified method of beam propagation and its application to distribution calculation in waveguides with a changing profile of an indicator of refraction / A.V. Gavrilov // Computer Optics. – 2008. – V. 32, N 1. – P. 15-22. – (In Russian).
  5. Yu, W. Parallel finite-difference time-domain method. / Wenhua Yu, Raj Mittra, Tao Su, Yongjun Liu, Xiaoling Yang. – Artech House electromagnetic analysis series, 2006. – 274 p.
  6. OlympIOs: design, simulation and mask layout platform //URL: http://www.c2v.nl/products/software/olympios-soft­ware.shtml.
  7. Elizarova, T.G. The use of multi-processor transputer system for solving mathematical physics / T.G. Elizarova B.N. Chetverushkin // Mathematical modelling. – 1992. – V. 4, N 11. – P. 75-100. – (In Russian).
  8. Golovashkin, D.L. Parallel algorithms of the grid equations decision of the three-diagonal kind based on a method of counter proraces / D.L. Golovashkin // Mathematical modelling. – 2005. – V. 17, N 11. – P. 118-128. – (In Russian).
  9. Tsukerman, I. Computational Methods for Nanoscale Applications. Particles, Plasmons and Waves / Igor Tsukerman. – Springer Science, 2005. – 530 p.
  10. Shmakov, V.A. Power Optics / VA. Shmakov; otv.red. V.I. Savin. - Moscow: “Nauka” Publisher, 2004. - 418 p. – (In Russian).
  11. Samarskiy, A.A. Computer gear / A.A. Samarskiy, P.N. Vabishchevich. - Moscow: Editorial URSS, 2003. - 784 p. – (In Russian).
  12. Loganova, L.V. A parallel algorithms in the cyclic coun­ter-sweep method two-dimensional grid domains / L.V. Lo­ganova, D.L. Golovashkin // Computational Technology. – 2011. – V. 16, N 4. – P. 64-71. – (In Russian).
  13. NVIDIA CUDA. Version 3.0. Reference Manual. February, 2010.
  14. Alekseev, V.A. Vector beam propagation method and its implementation technology CUDA / V.A. Alekseev, D.L. Golovashkin // Computer Optics. - 2010. – V. 34, ¹ 2. – P. 225-229. – (In Russian).
  15. Samarskiy, A.A. Methods of the decision of the grid equations / A.A. Samarskiy, E.S. Nilolayev. – Moscow: “Nauka” Publisher, 1978. – 561 p. – (In Russian).
  16. Antonov, A.S. Parallel programming using technology OpenMP: Textbook / A.S. Antonov. – Ìoscow: MSU publishing house, 2009. – 77 p.– (In Russian).
  17. Boreskov, A.V. Technology basics CUDA / A.V. Bores–kov, A. Kharlamov. – Moscow: DMK Press Publisher, 2010. – 232 p. – (In Russian).
  18. Ortega, Dg.M. Introduction in parallel and vector methods of linear systems decision / Dgaims M. Ortega, translate from English H.D. Ikramova, I.E. Kaporina; edited by H.D. Ikra­mo­va. – Moscow: “Mir” Publisher, 1991. – 364 p. – (In Russian).
  19. Andrew Davidson, Yao Zhang, John D. Owens An Auto-tuned Method for Solving Large Tridiagonal Systems on the GPU Published in: IPDPS '11: Proceedings of the 2011 IEEE International Parallel & Distributed Processing Symposium IPDPS '11 Proceedings of the 2011 IEEE International Parallel & Distributed Processing Symposium Pages 956-965 IEEE Computer Society Washington, DC, USA ©2011.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20