Implementation of FDTD-method by means of CUDA-technology

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Abstract

This paper deals with the implementation of the vector FDTD-method for solving of combined Maxwell’s equations on GPU. The implementation of the algorithm for two-dimensional problem on graphics processor NVIDIA GeForce GT 240 using CUDA-technology demonstrates computational speedup in 42.9 times as against with computations has been made on central processor  Intel Core Duo E6500. The future prospects of mesh domain decomposition application are considered in this article for the implementation of the vector FDTD-method on GPU.

About the authors

D. L. Golovashkin

Image Processing Systems Institute of RAS, Samara

Author for correspondence.
Email: dimitriy@smr.ru

 Doctor of Physical and Mathematical Sciences, Professor

Senior Researcher

Russian Federation

S. A. Malysheva

Samara State Aerospace University

Email: s-a-mal@yandex.ru

Student

Russian Federation

References

  1. Methods for Computer Design of Diffractive Optical Elements / edited by Victor A. Soifer. – New York: John Wiley & Sons, Inc., 2002. – 765 p.
  2. Diffractive Computer Optics / edited by Victor A. Soifer. – Moscow: “Fizmatlit” Publisher, 2007. – 736 p. – (in Russian].
  3. Kazanskiy, N.L. 70th Anniversary of Professor Iosif Norairovich Sisakian / N.L. Kazanskiy // Bulletin of Samara State Aerospace University. – 2008. – N 2(15). – P. 9-34.
  4. Kazanskiy, N.L. R-D Center for Solving the Computer Optics Problems / N.L. Kazanskiy // Computer Optics. – 2006. – N 29. – P. 58-77. – [in Russian].
  5. Pavelyev, V.S. Diffractive Microoptics for Technological IR-Lasers / V.S. Pavelyev, V.A. Soifer, V.I. Konov, V.V. Kononenko, A.V. Volkov // in book: “High-Power and Femtosecond Lasers: Properties, Materials and Applications”, Editors: Paul-Henri Barret and Michael Palmer. – Nova Science Publishers, Inc., 2009. – P. 125-158.
  6. Kazanskiy, N.L. Optical Microrelief Forming in Outside-Electrode Plasma of HighVoltage Gas Discharge / N.L. Kazanskiy, V.A. Kolpakov. – Moscow: “Radio & Svyaz” Publisher, 2009. – 220 p. – [in Russian].
  7. Kazanskiy, N.L. Computer-aided design of diffractive optical elements / N.L. Kazanskiy, V.V. Kotlyar, V.A. Soifer // Optical Engineering. – 1994. – Vol. 33, N 10. – Р. 3156-3166.
  8. Soifer, V.A. Iterative methods for diffractive optical elements computation / V.A. Soifer, V.V. Kotlyar, L.L. Doskolovich. – London: Taylor and Francis, 1997. – 250 p.
  9. Golub, M.A. Computational experiment with plane optical elements / M.A. Golub, N.L. Kazanskii, I.N. Sisakyan, V.A. Soifer // Optoelectronics, Instrumentation and Data Processing. – Allerton Press, 1988. – N 1. – P. 78-89.
  10. Kazanskiy, N.L. Mathematical Simulation of Optical Systems / N.L. Kazanskiy. – Samara: “SSAU” Publisher, 2005. – 240 p. – [in Russian].
  11. Volkov, A.V. Fabricating and Testing Diffractive Optical Elements Focusing into a Ring and into a Twin-Spot / A.V. Volkov, N.L. Kazanskiy, G.V. Uspleniev // Computer Optics. – 1999. – N 19. – P. 132-136. – [in Russian].
  12. Volkov, A.V. Investigation of Lighting Devices Based on Diffractive Optical Elements / A.V. Volkov, N.L. Kazanskiy, G.V. Uspleniev // Computer Optics. – 1999.– N 19.– P. 137-142. – [in Russian].
  13. Volkov, A.V. Design and Testing Binary Focusers for High-Power ND-YAGLaser / A.V. Volkov, L.L. Doskolovich, N.L. Kazanskiy, G.V. Uspleniev, A. Zanelli // Computer Optics. – 2000. – N 20. – P. 84-89. – [in Russian].
  14. Doskolovich, L.L. Design and investigation of color separation diffraction gratings / L.L. Doskolovich, N.L. Kazanskiy, S.N. Khonina, R.V. Skidanov, N. Heikkila, S. Siitonen, and J. Turunen // Applied Optics. – 2007. – Vol. 46, N 15. – Р. 2825-2830.
  15. Skidanov, R.V. Optical Micromanipulation with Employment of Microblasts of Microparticles of Polystyrene / R.V. Skidanov, A.A. Morozov // Computer Optics. – 2010. – Vol. 34, N 3. – P. 302-307. – [in Russian].
  16. Doskolovich, L.L. Focusators for laser-branding / L.L. Doskolovich, N.L. Kazanskiy, S.I. Kharitonov, G.V. Usplenjev // Optics and Lasers in Engineering. – 1991. – Vol. 15, N 5. – P. 311-322.
  17. Kazanskiy, N.L. Formation of the Desired Energy Impact During Laser Processing of Materials Using the Radiation Focusers / N.L. Kazanskiy, S.P. Murzin, S.Yu. Klochkov // Computer Optics. – 2005. – Vol. 28. – P. 89-93. – [in Russian].
  18. Kazanskiy, N.L. Application of the Radiation Focusers During the Formation of Nanoporous Structures of Solid-Crystalline Materials / N.L. Kazanskiy, S.P. Murzin, V.I. Tregub, A.V. Mezhenin // Computer Optics. – 2007. – Vol. 31, N 2. – P. 48-51. – [in Russian].
  19. Kazanskiy, N.L. Laser Radiation Formation for Creation Nanodimentional Porous Structures of Materials / N.L. Kazanskiy, S.P. Murzin, A.V. Mezhenin, E.L. Osetrov // Computer Optics. – 2008. – Vol. 32, N 3. – P. 246-248. – [in Russian].
  20. Karpeev, S.V. Fibre sensors based on transverse mode selection / S.V. Karpeev, V.S. Pavelyev, S.N. Khonina, N.L. Kazanskiy, A.V. Gavrilov, V.A. Eropolov // Journal of Modern Optics. – 2007. – Vol. 54, No. 6. – Р. 833-844.
  21. Koronkevich, V.P. Laser Interferometric and Diffractive Systems / V.P. Koronkevich, A.G. Poleschuk, A.G. Sedukhin, G.A. Lenkova // Computer Optics. – 2010. – Vol. 34, N 1. – P. 4-23. – [in Russian].
  22. Shiono, T. Planar-optic-disk pickup with diffractive micro-optics / T. Shiono, T. Ogawa // Applied Optics. – 1994. – Vol. 33, N 31. – Р. 7350-7355.
  23. Soifer, V.A. Nanophotonics and Diffractive Optics / V.A. Soifer // Computer Optics. – 2008. – Vol. 32, N 2. – P. 110-118. – [in Russian].
  24. Soifer, V.A. Diffractive Optical Elements in Nanophotonic Devices / V.A. Soifer, V.V. Kotlyar, L.L. Doskolovich // Computer Optics. – 2009. – Vol. 33, N 4. – P. 352-368. – [in Russian].
  25. Kotlyar, V.V. Numerical Solution of Maxwell’s Equations in the Diffractive Optics Problems / V.V. Kotlyar // Computer Optics. – 2006. – Vol. 29. – P. 24-40. – [in Russian].
  26. Yee, K.S. Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media / K.S. Yee // IEEE Trans. Antennas Propag., 1966.– AP-14.– P. 302-307.
  27. Taflove, A. Computational Electrodynamics: The Finite-Difference TimeDomain Method: 2nd. ed. / A. Taflove, S. Hagness – Boston: Arthech House Publishers, 2000. – 852 p.
  28. Judkins, J.B. Finite-Difference Time-Domain Modeling of Nonperfectly Conducting Metallic Thin-Film Gratings / J.B. Judkins and R.W. Ziolkowski // J. Opt. Soc. Am. A. – 1995. – Vol. 12, N 9. – P. 1974-1983.
  29. Golovashkin, D.L. Modeling of Waveguide Propagation of Optical Radiation in the Frame of Electromagnetic Theory / D.L. Golovashkin, A.A. Degtyarev, V.A. Soifer // Computer Optics. – 1997. – Vol. 17. – P. 5-9. – [in Russian].
  30. Prather, DW. Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements / Dennis W. Prather and Shouyuan Shi // J. Opt. Soc. Am. A. – 1999. – Vol. 16, N 5. – Р. 1131-1142.
  31. Mirotznik, M.S. ThreeDimensional Analysis of Subwavelength Diffractive Optical Elements with the FiniteDifference Time-Domain Method / Mark S. Mirotznik, Dennis W. Prather, Joseph N. Mait, William A. Beck, Shouyuan Shi, and Xiang Gao // Applied Optics. – 2000. – Vol. 39, N 17. – Р. 2871-2880.
  32. Golovashkin, D.L. Using the Finite-Difference Method for Solving the Problem of H-Wave Diffraction with TwoDimensional Dielectric Gratings / D.L. Golovashkin, N.L. Kazanskiy, V.N. Safina // Computer Optics. – 2003. – Vol. 25. – P. 36-40. – [in Russian].
  33. Golovashkin, D.L. Diffraction of TE-wave on two-dimension ideal comducte gread / D.L. Golovashkin // Mathematical Modeling. – 2005. – Vol. 17, N 4. – P. 53-61. – [in Russian].
  34. Golovashkin, D.L. Incident Wave Source Conditions for the Finite-Difference Time-Domain Metod: One-Domensional Formulation / D.L. Golovashkin, N.L. Kazanskiy // Optoelectronics, Instrumentation and Data Processing, Allerton Press Inc. – 2006. – Vol. 42, N 6. – P. 78-85.
  35. Golovashkin, D.L. Incident Wave Source Conditions for the Finite-Difference Time-Domain Metod: Two-Domensional Formulation / D.L. Golovashkin, N.L. Kazanskiy // Optoelectronics, Instrumentation and Data Processing, Allerton Press Inc. – 2007. – Vol. 43, N 6. – P. 547-555.
  36. Golovashkin, D.L. Solving Problems of Computer Optics on Graphical Computing Devices / D.L. Golovashkin, N.L. Kazanskiy // in book: «Advantage Information Technologies for Aviation and Space (AIT-2010). Selected Papers of the International Conference with Elements of a Scientific School for Young People». – Samara: “SSAU” Publisher, 2010. – P. 512-516. – [in Russian].
  37. Fidel, B. Hybrid ray-FDTD moving window approach to pulse propagation / B. Fidel, E. Heyman, R. Kastner and R.W. Ziolkowski // Journal of Computational Physics. – 1997. – Vol. 138, Issue 2. – Р. 480-500.
  38. Perlik, A.T. Predicting scattering of electromagnetic fields using FD-TD on a connection machine / A.T. Perlik, А. Taflove, T. Opsahl // IEEE Transactions on magnetic. – 1989.– Vol. 25, N 4. – Р. 2910-2912.
  39. Yu, W. Parallel Finite-Difference Time-Domain Method / W. Yu, R. Mittra, T. Su, Y. Liu, H. Yang – Boston: Arthech House Publishers, 2006. – 272 p.
  40. Price, D.K. GPU-based accelerated 2D and 3d FDTD solvers / D.K. Price, J.R. Humphrey and E.J. Kelmelis – Physics and Simulation of Optoelectronic Devices XV, vol. 6468 of Proceedings of SPIE, San Jose, CA, USA, January 2007.
  41. Adams, S. Finite Difference Time Domain (FDTD Simulations Using Graphics Processors / S. Adams, J. Payne, R. Boppana // Proceedings of the 2007 DoD High Performance Computing Modernization Program Users Group Conference, 2007. – Р. 334-338
  42. NVIDIA: Nvidia CUDA Compute Unified Device Architecture. Programming Guide version 2.3. – 2007.
  43. Valcarce, A. A GPU approach to FDTD for Radio Coverage Prediction / A. Valcarce, G. De La Roche, J. Zhang // IEEE 11th International Conference on Communication Systems, November 2008.
  44. Valcarce, A. Applying FDTD to the Coverage Prediction of WiMAX Femtocells / A. Valcarce, G. De La Roche, J. Zhang // EURASIP Journal on Wireless Communications and Networking, February 2009.
  45. Born, М. Principles of Optics / М. Born, E. Wolf. Fourth edition. – “Pergamon Press” Publisher, 1968. – 720 p.
  46. Golub, G. Matrix Computations / G. Golub, C. Van Loan – Мoscow: “Mir” Publisher, 1999. – 548 p. – [in Russian].
  47. NVIDIA: CUBLAS Library version 2.3. – 2007.
  48. Golovashkin, D.L. Mesh Domain Decomposition in the Finite-Difference Solution of Maxwell’s Equations / D.L. Golovashkin, N.L. Kazanskiy // Mathematical Modeling. – 2007. – Vol. 19, N 2. – P. 48-58. – [in Russian].

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