Skip to main content
SpringerLink
Log in

A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched layers previously developed for the Helmholtz equation is adapted for the popular Yee grid scheme for wave propagation in inhomogeneous, anisotropic media. Preliminary numerical results are presented for typical examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Champagne N J, Berryman J G, Buettner H M. FDFD: A 3D Finite-difference frequency-domain code for electromagnetic induction tomography. J Comput Phys, 2001, 170(2): 830–848

    Article  MathSciNet  MATH  Google Scholar 

  2. Chew W C, Jin J, Michielssen E, Song J. Fast and Efficient Algorithms in Computational Electromagnetics. London: Artech House, 2001

    Google Scholar 

  3. Chew W C, Weedon W H. A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. Microwave Opt Tech Lett, 1994, 7(13): 599–604

    Article  Google Scholar 

  4. Engquist B, Majda A. Absorbing boundary conditions for the numerical simulation of waves. Math Comp, 1977, 31: 629–651

    Article  MathSciNet  MATH  Google Scholar 

  5. Engquist B, Ying L. Sweeping preconditioner for the Helmholtz equation: hierarchical matrix representation. Comm Pure Appl Math, 2011, 64: 697–735

    Article  MathSciNet  MATH  Google Scholar 

  6. Engquist B, Ying L. Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers. Multiscale Model Simul, 2011, 9: 686–710

    Article  MathSciNet  MATH  Google Scholar 

  7. Jin J. The Finite Element Method in Electromagnetics. Hoboken: Wiley-IEEE Press, 2002

    MATH  Google Scholar 

  8. Lin L, Lu J, Ying L, Car R, E W. Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Commun Math Sci (to appear)

  9. Mur G. Absorbing boundary conditions for the finite-difference approximation of timedomain electromagnetic field equations. IEEE Trans Electromag Compat, 1981, 23: 377–382

    Article  Google Scholar 

  10. Taflove A, Hagness S. Computational Electrodynamics: the Finite-difference Timedomain Method. London: Artech House, 2005

    Google Scholar 

  11. Werner G R, Cary J R. A stable FDTD algorithm for non-diagonal, anisotropic dielectrics. J Comput Phys, 2007, 226(1): 1085–1101

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ICES, University of Texas at Austin, Austin, TX, 78712, USA

    Paul Tsuji & Lexing Ying

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    Lexing Ying

Authors
  1. Paul Tsuji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lexing Ying
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lexing Ying.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsuji, P., Ying, L. A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations. Front. Math. China 7, 347–363 (2012). https://doi.org/10.1007/s11464-012-0191-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-012-0191-8

Keywords

MSC

Search

Navigation