Joint finite – difference solution of the d’alembert and maxwell’s equations. Two – dimensional case
E.Yu. Buldygin, D.L. Golovashkin, L.V. Yablokova

Full text of article: Russian language.

Abstract:
The technique of searching of the collateral finite – difference solution of a wave equation and set of equations of Maxwell is offered, allowing to combine advantage and to avoid shortcomings of both made mention numerical methods of nanophotonics (to reduce expenses of memory and to apply well-known TF/SF and PML techniques). In a two – dimensional case on test examples convergence of such decision, possibility of imposing of PML-ayers and a task of an incident wave on the TF/SF technology are shown.

Key words:
D’Alembert equation, Maxwell’s equations, difference scheme, PML-layer, TF/SF technique.

References:

  1. Diffraction nanophotonics / edited by V.A. Soifer – Moscow: “Fizmatlit” Publisher, 2011. – 680 p. – (In Russian).
  2. Taflove, A. Computational Electrodynamics: The Finite-Difference Time-Domain Method: / A. Taflove, S. Hagness. – 3-d. ed. – Boston: Arthech House Publishers. – 2005. – 852 p.
  3. Yu, W. Parallel finite-difference time-domain method / Wenhua Yu, Raj Mittra, Tao Su, Yongjun Liu, Xiaoling Yang // ARTECH HOUSE, INC – Boston, 2006. – 262 p.
  4. Elsherbeni, A. The Finite Difference Time Domain Method for Electromagnetics: With MATLAB Simulations / Atef Elsherbeni, Demir Veysel – SciTech Publishing, 2009. – 450 .
  5. http: // ab-initio.mit.edu / wiki / index.php / Meep.
  6. http: // b-calm.sourceforge.net .
  7. Fidel, B. Hybrid ray – FDTD moving window approach to pulse propagation / B. Fidel, E. Heyman, R. Kastner, R.W. Zioklowski // Journal of Computational Physics. – 1997. – Vol. 138, Issue 2. – P. 480–500.
  8. Shi, S. Analysis of diffractive optical elements using a nonuniform finite – difference time – domain method / S. Shi, X. Tao, L. Yang, D.W. Prather // Optical Engineering. – 2001. – Vol. 40, 4. – P. 503–510.
  9. Golovashkin, D.L. Mesh Domain Decomposition in the Finite-Difference Solution of Maxwell’s Equations / D.L. Go­lovashkin, N. L. Kazanskiy // Optical Memory & Neural Networks (Information Optics). – 2009. – Vol. 18,  3P. P. 203-211.
  10. Golovashkin, D.L. Solution of difference equations in graphical computing devices. Method of pyramids. / D.L. Golovashkin, A.V. Kochurov // Computing Technologies. – 2012. – Vol. 17, N 3. – P.55–69. – (In Russian).
  11. Mur, G. Absorbing boundary conditions for the finite –difference approximation of the time – domain electromagnetic field equations / G. Mur / IEEE Trans. Electromagnetic Compability. – 1981. – Vol. 23. – P. 377–382.
  12. Kozlova, E.S. Model operation of distribution of a short twodimensional impulse of light / E.S. Kozlova, V.V. Kotlyar // Computer Optics. – 2012. – Vol. 36, N 2. – P. 158–64. – (In Russian).
  13. Kozlova, E.S. Simmulations of Sommerfeld and Brillouin precursorsin the medium with frequency dispersion using numerical method of solving wave equations / E.S. Kozlova, V.V. Kotlyar // Computer Optics. – 2013. – Vol. 37, N 2. – P. 146–154. – (In Russian).
  14. Golovashkin, D.L. Joint finite-difference solution of the Dalamber and Maxwell’s equations. One – dimensional case / D.L. Golovashkin, L.V. Yablokova // Computer Optics. – 2012. – Vol. 36, N 4. – P. 527–533. – (In Russian).
  15. Vaganov, R.B. Fundamentals of the theory of diffraction / R.B. Vaganov, B.Z. Kacenelenbaum – Moskow: “Nauka” Publisher, 1982 – 272 p. – (in Russian).
  16. Berenger, J.-P. A perfectly matched layer for the absorption of electromagnetic waves / Jean-Pierre Berenger // Journal of Computational Physics. – 1994. –  114. – P. 185–200.
  17. Ortega, M. Introduction to Parallel and Vector Solution of Linear Systems / M. Ortega. – Plenum Press, New York, USA, 1988. – 364 p.
  18. Golovashkin D.L. Statement of radiating conditions at work modeling of cylindrical diffractive optical elements using differential solutions of Maxwell's equations / D.L. Golovashkin // athematic Modeling. – 2007. – Vol 19, N 3. – P. 3–14. – (In Russian).
  19. Golovashkin, D.L. Technique of formation of the incident wave at the difference solution of Maxwell's equations (two-dimensional case) / D.L. Golovashkin, N. L. Kazanskiy // Optoelectronics, Instrumentation and Data Processing. – 2007. – Vol. 43, N 6. – P. 78–88. – (In Russian).

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