Block algorithms of a simultaneous difference solution of d’Alembert's and Maxwell's equations
Yablokova L.V., Golovashkin D.L.

Samara National Research University, Samara, Russia,
Image Processing Systems Institute оf RAS – Branch of the FSRC "Crystallography and Photonics" RAS, Samara, Russia


The work is devoted to the synthesis of block algorithms of the FDTD method. In particular, the simultaneous difference solution of d’Alembert's and Maxwell's equations is considered. Accounting for the computer memory hierarchical structure allows the calculation time to be reduced up to six times when compared with the known software implementations of the method.

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

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.


  1. Voevodin VV. Mathematical models and methods in parallel processes [In Russian]. Moscow: "Nauka" Publisher; 1986.
  2. Shen JP, Lipasti MH. Modern processor design: Fundamentals of superscalar processors. 2nd ed. Long Grove, Illinois: Waveland Press, Inc; 2013. ISBN: 978-1-4786-0783-0.
  3. Cron G. Equivalent circuit of the field equations of Maxwell. Proc IRE 1944; 32(5): 289-299. DOI: 10.1109/JRPROC.1944.231021.
  4. Yu W, Mittra R, Su T, Liu Y, Yang X. Parallel finite-difference time-domain method. Boston: Artech House; 2006. ISBN: 978-1-59693-085-8.
  5. Jordan HF, Bokhari S, Staker S, Sauer JR, ElHelbawy MA, Piket-May MJ. Experience with FDTD techniques on the Cray MTA supercomputer. Proc SPIE 2001; 4528: 68-76. DOI: 10.1117/12.434878.
  6. Inman MJ, Elsherbeni AZ. Optimization and parameter exploration using GPU based FDTD solvers. IEEE MTT-S International Microwave Symposium Digest 2008: 149-152. DOI: 10.1109/MWSYM.2008.4633125.
  7. Waidyasooriya HM, Hariyama M. FPGA-based deep-pipelined architecture for FDTD acceleration using OpenCL. ICIS 2016: 109-114. DOI: 10.1109/ICIS.2016.7550742.
  8. Golub GH, Van Loan ChF. Matrix Computations. 3rd ed. Baltomore, London: Johns Hopkins University Press; 1996. ISBN: 0-8018-5414-8.
  9. Demmel J. Applied numerical linear algebra. Philadelphia: SIAM; 1997. ISBN: 0-89871-389-7.
  10. Wolfe M. More iteration space tiling. Proc Supercomputing '89 1989: 655-664. DOI: 10.1145/76263.76337.
  11. Perepelkina AYu, Levchenko VD. DiamondTorre algorithm for high-performance wave modeling. Keldysh Institute Preprints 2015; 18: 1-20.
  12. Orozco D, Guang G. Mapping the FDTD application to many-core chip architectures. ICPP '09 2009: 309-316. DOI: 10.1109/ICPP.2009.44.
  13. Golovashkin DL, Yablokova LV. Joint finite-difference solution of the Dalamber and Maxwell's equations. One-dimensional case. Computer Optics 2012; 36(4): 527-533.
  14. Buldygin EYu, Golovashkin DL, Yablokova LV. Joint finite-difference solution of the D'Alembert and Maxwell's equations. Two-dimensional case [In Russian]. Computer Optics 2014; 38(1): 20-27.
  15. Markov AA, Nagorny NM. The theory of algorithms. Dordrecht, Netherlands: Springer, 1988. ISBN: 978-90-277-2773-2.
  16. Golovashkin DL, Kazansky NL, Safina VN. Use of the finite-difference method for solving the problem of H-wave diffraction by two-dimensional dielectric gratings. Optical Memory and Neural Networks 2004; 13(1): 55-62.
  17. Kozlova ES, Kotlyar VV. ‎Simmulations of Sommerfeld and Brillouin precursors in the medium with frequency dispersion using numerical method of solving wave equations [In Russian]. Computer Optics 2013; 37(2): 146-154.
  18. Elsherbeni AZ, Demir V. The ?nite-difference time-domain method for electromagnetics with MATLAB simulations. Ralrigh, NC: SciTech Publishing Inc 2009. ISBN: 978-1-891121-71-5.
  19. Taflove A, Hagness S. Computational electrodynamics: The finite-difference time-domain method. 3th ed. Boston: Arthech House Publishers, 2005. ISBN: 978-1-58053-832-9.
  20. Oskooi AF, Roundyb D, Ibanescua M, Bermel P, Joannopoulos JD, Johnson SG. MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method. Comput Phys Commun 2010; 181(3): 687-702. DOI: 10.1016/j.cpc.2009.11.008.
  21. Plokhotnikov KE. Computational methods: Theory and practice in the MATLAB environment. The course of lectures [In Russian]. Moscow: "MGU" Publisher; 2007.
  22. Certificate of state registration of the computer program No. 2017613903 "Joint difference solution of the d'Alembert and Maxwell equations" [In Russian].
  23. Golovashkin DL. Formulation of the radiation condition for modeling the cylindrical doe operation using a finite difference solution of Maxwell's equations. Matem Mod 2007; 19(3): 3-14.
  24. Foster I. Designing and building parallel programs: Concepts and tools for parallel software engineering. Boston, MA: Addison-Wesley Longman Publishing; 1995. ISBN: 978-0-2015-7594-1.
  25. Samarskii AA. The theory of difference schemes. New York, NY: Marcel Dekker Inc; 2001. ISBN: 978-0-8247-0468-1.
  26. Gallivan K, Jalby W, Meier U, Sameh AH. Impact of hierarhical memory system on linear algebra algorithm design. The International Journal of Supercomputer Applications 1988; 2(1): 12-48. DOI: 10.1177/109434208800200103.
  27. Wolfe M. Loops skewing: The wavefront method revisited. International Journal of Parallel Programming 1986; 15(4): 279-293. DOI: 10.1007/BF01407876.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20