Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 89, 2012 - Issue 10
Submit an article Journal homepage
204
Views
2
CrossRef citations to date
0
Altmetric
Section B

A second-order scheme for Maxwell's equations with dielectric permittivity discontinuities and total field-scattered field boundaries

Timur Z. Ismagilov Novosibirsk State University, Pirogova 2, Novosibirsk, 630090, RussiaCorrespondence[email protected]
Pages 1378-1387 | Received 27 Oct 2011, Accepted 28 Mar 2012, Published online: 14 May 2012

References

  • Chung , E. T. , Du , Q. and Zou , J. 2003 . Convergence analysis on a finite volume method for Maxwell's equations in non-homogeneous media . SIAM J. Numer. Anal. , 41 : 37 – 63 .
  • Chung , E. T. and Engquist , B. 2005 . Convergence analysis of fully discrete finite volume methods for Maxwell's equations in nonhomogeneous media . SIAM J. Numer. Anal. , 43 : 303 – 317 .
  • Cioni , J.-P. , Fezoui , L. and Issautier , D. 1994 . Higher order upwind schemes for solving time domain Maxwell equations . La Recherche Aĕrospatiale , 5 : 319 – 328 .
  • Geuzaine , C. and Remacle , J.-F. 2009 . Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities . Int. J. Numer. Meth. Eng. , 3 : 1 – 24 .
  • Godunov , S. K. 1959 . A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations . Math. Sbornik , 47 : 271 – 306 .
  • Hermeline , F. 1993 . Two coupled particle-finite volume methods using Dalaunay–Voronoi meshes for approximation of Vlasov–Poisson and Vlasov–Maxwell equations . J. Comput. Phys. , 106 : 1 – 18 .
  • Ismagilov , T. Z. 2010 . Parallel algorithm for numerical solution of three-dimensional Maxwell's equations with discontinuous dielectric permittivity on tetrahedral meshes [In Russian] . USATU Vestnik , 14 : 152 – 159 .
  • Ismagilov , T. Z. and Gorbachev , A. I. 2011 . Parallel algorithm for numerical solution of three-dimensional Maxwell's equations with discontinuous dielectric permittivity on prismatic meshes [In Russian] . Comp. Meth. Progr. , 12 : 128 – 136 .
  • Laub , A. J. 2004 . Matrix Analysis for Scientists and Engineers , Philadelphia : SIAM .
  • Lax , P. D. and Wendroff , B. 1960 . Systems of conservation laws . Commun. Pure Appl. Math. , 13 : 217 – 237 .
  • Lebedev , A. S. , Fedoruk , M. P. and Shtyrina , O. V. 2006 . Finite volume algorithm for solving the time-dependent Maxwell equations on unstructured meshes . J. Comput. Math. Math. Phys. , 47 : 1219 – 1233 .
  • Shankar , V. , Hall , W. F. and Mohammadian , A. H. 1989 . “ A CFD-based finite-volume procedure for computational electromagnetics – interdisciplinary applications of CFD methods ” . 551 – 564 . AIAA A89-41776 18-02
  • Stratton , J. A. 1941 . Electromagnetic Theory , NewYork : McGraw Hill .
  • Sullivan , D. M. 2000 . Electromagnetic Simulation Using the Finite-Difference Time-Domain Method , New York : IEEE .
  • Taflove , A. and Hagness , S. C. 2000 . Computational Electrodynamics: The Finite-Difference Time-Domain Method , Boston : Artech House .
  • Van Leer , B. 1979 . Towards the ultimate conservative difference scheme. A second order sequel to Godunov's method . J. Comput. Phys. , 32 : 101 – 136 .
  • Yee , K. S. 1966 . Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media . IEEE Trans. Antennas Propagat. , 17 : 585 – 589 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.