Nanophotonics integrated circuits simulation: FDTD method
Abstract
This paper considers the functionality of FDTD (Finite difference time-domain) method for parallel computing; the main difficulties that arise in its practical use are listed; a comparison with other numerical methods of electromagnetic phenomena simulation is made. The requirements to performance balance of supercomputer node, at which effective implementation of the parallel version of FDTD method is possible, are specified. The need for computing at exaflops scale for solving the tasks of integral nanophotonics is shown, an approach to solving such problems is proposed.
Supporting agencies: The authors express their gratitude to the Ministry of Education of the Russian Federation for financial support of research within the framework of the grant of the Government of the Russian Federation for state support of scientific research conducted under the supervision of leading scientists in Russian educational institutions of higher professional education, as well as to A.V. Bukhanovsky for discussing the work
About the Authors
K. S. Ladutenko
Ioffe Physical-Technical Institute of the Russian Academy of
Sciences
Russian Federation
Russian Federation
Konstantin Ladutenko, junior research fellow
Saint Petersburg
P. A. Belov
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics
Russian Federation
Russian Federation
Pavel Belov, chief research fellow, Doctor of Science
Saint Petersburg
References
1. Taflove A., Hagness S. C. Computational Electrodynamics: the Finite-Difference Time-Domain Method. — 3<sup>rd</sup> edition. — Artech House, 2005.
2. Гельфонд А. О. Исчисление конечных разностей. — 2-ое изд. — М. : ФМЛ, 1959.
3. Самарский А. А. Введение в теорию разностных схем. — М. : Наука, 1971.
4. Yee K. Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media // IEEE Trans. on Antennas and Propagation.— 1966.— V. AP14, № 3. — P. 302–307.
5. Mur G. Absorbing Boundary Conditions for the FiniteDifference Approximation of the TimeDomain ElectromagneticField Equations // IEEE Trans. on Electromagnetic Compatibility. — 1981. — V. EMC23, № 4. — P. 377–382.
6. Higdon R. L. Absorbing Boundary Conditions for Difference Approximations to the MultiDimensional Wave Equation // Mathematics of Computation. — 1986. — V. 47, № 176. — P. 437–459.
7. Ramahi O. M. The Concurrent Complementary Operators Method for FDTD Mesh Truncation // IEEE Trans. on Antennas and Propagation. — 1998. — V. 46, № 10. — P. 1475–1482.
8. Berenger J.P. A Perfectly Matched Layer for the Absorption of Electromagnetic Waves // J. of Computational Physics. — 1994. — V. 114, № 2. — P. 185–200.
9. Gedney S. D. An Anisotropic PML Absorbing Media for the FDTD Simulation of Fields in Lossy and Dispersive Media // Electromagnetics. — 1996. — V. 16, № 4. — P. 399–415.
10. Roden J. A., Gedney S. D. Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media // Microwave and Optical Technology Lett. — 2000. — V. 27, № 5. — P. 334–339.
11. Teixeira F. L. On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves // Radio Science. — 2003. — V. 38, № 2. - P. 8014.
12. Moore G. Cramming more components onto integrated circuits // Electronics Magazine. — 1965. — V. 38, № 8. — P. 4.
13. Yu W., Mittra R., Su T. et al. Parallel FiniteDifference TimeDomain Method. — Artech House, 2006.
14. Inan U. S., Marshall R. A. Numerical Electromagnetics The FDTD Method. — Cambridge University Press, 2011.
15. URL: http://www.cvel.clemson.edu/modeling/index.html.
16. Bondeson A., Rylander T., Ingelstr¨om P. Computational Electromagnetics. — Springer, 2005.
17. Yu W., Yang X., Liu Y. et al. Advanced FDTD Methods: Parallelization, Acceleration, and Engineering Applications. — Artech House, 2011.
18. Ильин В. П. Об экзапроблемах математического моделирования // Тр. Параллельные вычислительные технологии — Уфа, Россия, 2010.
19. URL: http://abinitio.mit.edu/wiki/index.php/Meep.
20. URL: http://www.acceleware.com/fdtdsolvers.
21. URL: http://www.2comu.com/products_pc_cluster.html.
22. URL: http://www.photond.com/products/fdtd/fdtd02.htm.
23. URL: http://www.remcom.com/xf7mpi/.
24. URL: http://www.top500.org.
25. Amdahl G. M. Validity of the SingleProcessor Approach to Achieveing Large Scale Computing Capabilities // In Proc. AFIPS Conference. — 1967.
26. Gustafson J. L. Reevaluating Amdahl’s Law // Communications of the ACM. — 1988. — V. 31. — P. 532–533.
27. Hospodor A., Miller E. L. Interconnection Architectures for PetabyteScale HighPerformance Storage Systems // 12<sup>th</sup> NASA Goddard Conference on Mass Storage Systems and Technologies (MSST2004). — 2004.
28. Ajima Y., Sumimoto S., Shimizu T. Tofu: A 6d Mesh/torus Interconnect for Exascale Computers // Computer, IEEE Computer Society. — 2009. — V. 42, № 11. — P. 36–40.
29. Orcutt J. S., Khilo A., Holzwarth Ch. W. et al. Nanophotonic integration in stateoftheart CMOS foundries // Optics Express. — 2011. — V. 19, № 3. — P. 2335–2346.
30. Курант Р., Фридрихс К., Леви Г. О разностных уравнениях математической физики // УМН. — 1941. — № 8. — С. 125–160.
31. Potluri S., Lai P., Tomko K. et al. Quantifying Performance Benefits of Overlap using MPI2 in a Seismic Modeling Application // Proc. of the 24<sup>th</sup> ACM International Conference on Supercomputing. — 2010.
Review
For citations:
Ladutenko K.S., Belov P.A. Nanophotonics integrated circuits simulation: FDTD method. Nanosystems: Physics, Chemistry, Mathematics. 2012;3(5):42-61. (In Russ.)
Views:
22
Email this article 