Numerical simulation of 2D electrodynamic problems with unstructured triangular meshes
Fadeev D.A.


Institute of Applied Physics RAS, Nizhny Novgorod, Russia


We present a generalization of standard leap-frog plus Yee mesh approach for Cauchy problem in electrodynamics simulations on unstructured triangulated mesh. The presented approach still inherits from finite-difference time-domain and do not use techniques developed in finite-volume time-domain approach. In the paper the whole flow from mesh creation to actual simulation is presented. The proposed computation flow is parallel ready and can be implemented for distributed systems (computation servers, graphical processing units, etc.). We studied the influence of non-regular triangulation on stability and dispersion properties of numerical solution.

numerical approximation and analysis, mathematical methods in physics, computational electromagnetic methods

Fadeev DA. Numerical simulation of 2D electrodynamic problems with unstructured triangular meshes. Computer Optics 2019; 43(3): 385-390. DOI: 10.18287/2412-6179-2019-43-3-385-390.


  1. Yee KS. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans Antennas Propagat 1966; 14: 302.
  2. Kolesik M, Moloney JV. Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations. Phys Rev E 2004; 70: 036604.
  3. Skobelev SA, Kartashov DV, Kim AV. Few-optical-cycle solitons and pulse self-compression in a Kerr medium. Phys Rev Lett 2007; 99(20): 203902.
  4. Kosareva OG, Liu W. Panov NA, Bernhardt J, Ji Z, Sharifi M, Li R, Xu Z, Liu J, Wang Z, Ju J, Lu X, Jiang Y, Leng Y, Liang X, Kandidov VP, Chin SL. Can we reach very high intensity in air with femtosecond PW laser pulses? Laser Phys 2009, 19: 1776-1792.
  5. Dey I, Jana K, Fedorov VY, Koulouklidis AD, Mondal A, Shaikh M, Sarkar D, Lad AD, Tzortzakis S, Couairon A, and Kumar GR. Highly efficient broadband terahertz generation from ultrashort laser filamentation in liquids. Nature Communications 2017; 8: 1184.
  6. Déchard J, Debayle A, Davoine X, Gremillet L, Bergé L. Terahertz pulse generation in underdense relativistic plasmas: From photoionization-induced radiation to coherent transition radiation. Phys Rev Lett 2018; 120: 144801.
  7. Fadeev DA, Oladyshkin IV, Mironov VA. Terahertz emission from metal nanoparticle array. Opt Lett 2018; 43: 1939-1942.
  8. Nesterenko DV, Kotlyar VV. Hybrid finite element method and boundary element method for analysis of light diffraction on diffraction gratings [In Russian]. Computer Optics 2008; 32(3): 238-245.
  9. Sprangle P, Peñano JR, Hafizi B, Kapetanakos CA. Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces. Phys Rev E 2004; 69: 066415.
  10. Leuchtmann P, Fumeaux C, Baumann D. Comparison of errors and stability in FDTD and FVTD. Advances in Radio Science 2003; 1: 87-92.
  11. Fumeaux C, Baumann D, Sankaran K, Krohne K, Vahldieck R, Li E. The finite-volume time-domain method for 3D solutions of Maxwell’s equations in complex geometries: a review. Proceedings of the European Microwave Association 2007; 3: 136-146.
  12. Gansen A, Hachemi ME, Belouettar S, Hassan O, Morgan K. EM modelling of arbitrary shaped anisotropic dielectric objects using an efficient 3D leapfrog scheme on unstructured meshes. Comput Mech 2016; 58: 441-455.
  13. Keranen J, Kanagas J, Ahola A, Kettunen L. Implicit Yee-like scheme on tetrahedral mesh. IEEE Transactions on magnetics 2002; 38(2): 717-720.
  14. Monk P, Suli E. Error estimates for Yee's method on non-uniform grids. IEEE Transactions on Magnetics 1994; 30(5): 3200-3203.
  15. Taflove A, Hagness S. Computational electrodynamics: The finite-difference time-domain method. 3rd ed. Boston, London: Arthech House Publishers; 2005.
  16. Aurenhammer F, Klein R, Lee D-T. Voronoi diagrams and Delaunay triangulations. World Scientific; 2013. ISBN: 978-981-4447-63-8.
  17. Birdsall CK, Langdon AB. Plasma physics via computer simulations. McGraw-Hill Book Company; 1985: 56.
  18. Dynamics of EMP in the presence of metallic particle. Source: <>.
  19. Delaunay B. Sur la sphère vide. A la mémoire de Georges Voronoi, Bulletin de l'Académie des Sciences de l'URSS, Classe des sciences mathématiques et naturelles 1934; 6: 793-800.
  20. Why GitHub? Source code. Source: <>.

© 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