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Block algorithms to solve Zheng/Chen/Zhang's finite-difference equations
D.L. Golovashkin 1,2, N.D. Morunov 1, L.V. Yablokova 2

IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 899 kB

DOI: 10.18287/2412-6179-CO-837

Pages: 461-468.

Full text of article: Russian language.

This paper is devoted to the design of multiblock algorithms of the FDTD-method intended for computations based on a Zheng-Chen-Zhang implicit finite-difference scheme. Special emphasis is placed on experimental research of the designed algorithms and detecting specific features of the multiblock computing based on implicit finite-difference equations. The efficiency of the proposed approaches is proved by a six-fold speed-up of computations.

FDTD-method, block algorithms, tiling, computational speed-up.

Golovashkin DL, Morunov ND, Yablokova LV. Block algorithms to solve Zheng/Chen/Zhang's finite-difference equations. Computer Optics 2021; 45(3): 461-468. DOI: 10.18287/2412-6179-CO-837.

This work was supported by the Russian Foundation for Basic Research under grant 19-07-00423 А.


  1. Taflove A. Computational electrodynamics: The finite-difference time-domain method. Boston: Arthech House Publishers; 2005.
  2. Taflove A, Oskooi A, Johnson SG. Advances in FDTD computational electrodynamics: Photonics and nanotechnology. Boston: Arthech House Publishers; 2013.
  3. Yee KS. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans Antennas Propag 1966; AP-14: 302-307. DOI: 10.1109/TAP.1966.1138693.
  4. Namiki T. A new FDTD algorithm based on alternating-direction implicit method. IEEE Trans Microw Theory Tech 1999; 47: 2003-2007.
  5. Xie G, Huang Z, Fang M, Wu X. A unified 3–D ADI–FDTD algorithm with one-step leapfrog approach for modeling frequency-dependent dispersive media. Int J Numer Model El 2019; 33(2): 184940-184949. DOI: 10.1002/jnm.266610.
  6. Wanjun S, Hou Z. Analysis of electromagnetic wave propagation and scattering characteristics of plasma shealth via high order ADE-ADI FDTD. J Electromagn Waves Appl 2016; 30(10): 1321-1333. DOI: 10.1080/09205071.2016.1198727.
  7. Yao Z, Wang YE. 3D ADI-FDTD modeling of platform reduction with thin film ferromagnetic material. IEEE International Symposium on Antennas and Propagation (APSURSI) 2016: 2019-2020. DOI: 10.1109/APS.2016.7696716.
  8. Jordan H, Bokhari S, Staker S, Sauer J, ElHelbawy M, Piket-May M. Experience with ADI-FDTD techniques on the Cray MTA supercomputer. Proc SPIE 2001; 4528: 68-76. DOI: 10.1117/12.434878.
  9. Liu S, Zou B, Zhang L, Ren S. A multi-GPU accelerated parallel domain decomposition one-step leapfrog ADI-FDTD. IEEE Antennas Wirel Propag Lett 2020; 19(5): 816-820. DOI: 10.1109/LAWP.2020.2981123.
  10. Orozco D, Guang G. Mapping the FDTD application to many-core chip architectures. International Conference on Parallel Processing (ICPP '09) 2009: 309-316. DOI: 10.1109/ICPP.2009.44.
  11. Minami T, Hibino M, Hiraishi T, Iwashita T, Nakashima H. Automatic parameter tuning of threedimensional tiled FDTD kernel. High Performance Computing for Computational Science (VECPAR 2014) 2014: 284-297. DOI: 10.1007/978-3-319-17353-5_24.
  12. Golub GH, Van Loan CF. Matrix computations. Baltomore, London: Johns Hopkins University Press; 1996.
  13. Zhen F, Chen Z, Zhang J. Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method. IEEE Trans Microw Theory Tech 2000; 48(9): 1550-1558.
  14. Ortega J. Introduction to Parallel and Vector Solution of Linear Systems. New York: Plenum Press; 1988.
  15. Zhou X. Tiling optimizations for stencil computations. Source: <https://www.ideals.illinois.edu/bitstream/handle/2142/44340/Xing_Zhou.pdf>.
  16. Samarskii AA. The theory of difference schemes. New York: Marcel Dekker Inc; 2001.
  17. Samarskii AA, Vabishchevich PN. Computational heat transfer. Chichester: Wiley; 1995.
  18. Demmel J. Applied numerical linear algebra. Philadel-phia: SIAM; 1997.
  19. Yablokova LV, Golovashkin DL. Block algorithms of a simultaneous difference solution of d’Alembert's and Maxwell's equations. Computer Optics 2018; 42(2): 320-327. DOI: 10.18287/2412-6179-2018-42-2-320-327.
  20. Wolfe M. Loops skewing: The wavefront method revisited. Int J Parallel Program 1986; 15(4): 279-293. DOI: 10.1007/BF01407876.
  21. Zakirov AV, Levchenko VD, Perepelkina AYu, Zempo Y. DiamondTorre algorithm and high-performance implementation of the FDTD-method for supercomputers with graphics accelerators [In Russian]. Proc “Supercomputer days in Russia '16” 2016: 80-94.

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