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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 5 — Feb. 28, 2011
  • pp: 4618–4631

Stretched-coordinate PMLs for Maxwell’s equations in the discontinuous Galerkin time-domain method

Michael König, Christopher Prohm, Kurt Busch, and Jens Niegemann  »View Author Affiliations

Optics Express, Vol. 19, Issue 5, pp. 4618-4631 (2011)

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The discontinuous Galerkin time-domain method (DGTD) is an emerging technique for the numerical simulation of time-dependent electromagnetic phenomena. For many applications it is necessary to model the infinite space which surrounds scatterers and sources. As a result, absorbing boundaries which mimic its properties play a key role in making DGTD a versatile tool for various kinds of systems. Popular techniques include the Silver-Müller boundary condition and uniaxial perfectly matched layers (UPMLs). We provide novel instructions for the implementation of stretched-coordinate perfectly matched layers in a discontinuous Galerkin framework and compare the performance of the three absorbers for a three-dimensional test system.

© 2011 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis

ToC Category:
Physical Optics

Original Manuscript: December 3, 2010
Revised Manuscript: January 17, 2011
Manuscript Accepted: January 21, 2011
Published: February 24, 2011

Michael König, Christopher Prohm, Kurt Busch, and Jens Niegemann, "Stretched-coordinate PMLs for Maxwell’s equations in the discontinuous Galerkin time-domain method," Opt. Express 19, 4618-4631 (2011)

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  1. A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  2. J. S. Hesthaven, and T. Warburton, “Nodal high-order methods on unstructured grids–I. Time-domain solution of Maxwell’s equations,” J. Comput. Phys. 181, 186–221 (2002). [CrossRef]
  3. J. S. Hesthaven, and T. Warburton, Nodal Discontinuous Galerkin Methods—Algorithms, Analysis, and Applications (Springer, 2007). [PubMed]
  4. T. Lu, P. Zhang, and W. Cai, “Discontinuous Galerkin methods for dispersive and lossy Maxwell’s equations and PML boundary conditions,” J. Comput. Phys. 200, 549–580 (2004). [CrossRef]
  5. J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photonics Nanostruct. Fundam. Appl. 7, 2–11 (2009). [CrossRef]
  6. M. König, K. Busch, and J. Niegemann, “The discontinuous Galerkin time-domain method for Maxwell’s equations with anisotropic materials,” Photonics Nanostruct. Fundam. Appl. 8, 303–309 (2010). [CrossRef]
  7. A. Hille, R. Kullock, S. Grafström, and L. M. Eng, “Improving nano-optical simulations through curved elements implemented within the discontinuous Galerkin method computational,” J. Comput. Theor. Nanosci. 7, 1581–1586 (2010). [CrossRef]
  8. N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: the role of separation and relative orientation,” Opt. Express 18, 6545–6554 (2010). [CrossRef] [PubMed]
  9. J. Niegemann, W. Pernice, and K. Busch, “Simulation of optical resonators using DGTD and FDTD,” J. Opt. A, Pure Appl. Opt. 11, 114015 (2009). [CrossRef]
  10. T. Hagstrom, and S. Lau, “Radiation boundary conditions for Maxwell’s equations: A review of accurate timedomain formulations,” J. Comput. Math. 25, 305–336 (2007).
  11. J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
  12. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antenn. Propag. 43, 1460–1463 (1995). [CrossRef]
  13. W. C. Chew, and W. H. Weedon, “A 3D perfectly matched medium from modified maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994). [CrossRef]
  14. J.-P. Bérenger, Perfectly Matched Layer (PML) for Computational Electromagnetics (Morgan & Claypool Publishers, 2007).
  15. P. Monk, Finite Element Methods for Maxwell’s Equations (Oxford University Press, 2003). [CrossRef] [PubMed]
  16. M. H. Carpenter, and C. A. Kennedy, “Fourth-order 2N-storage Runge–Kutta schemes,” NASA Tech. Memo. 109112 (1994).
  17. R. Diehl, K. Busch, and J. Niegemann, “Comparison of low-storage Runge-Kutta schemes for discontinuous Galerkin time-domain simulations of Maxwell’s equations,” J. Comput. Theor. Nanosci. 7, 1572–1580 (2010). [CrossRef]
  18. R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems (Cambridge University Press, 2002). [CrossRef]

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