Perfectly matched layers for Maxwell's equations in second order formulation

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We consider the two-dimensional Maxwell's equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary condition are discretized to second order accuracy employing an embedded technique which does not suffer from a ''small-cell'' time-step restriction in the explicit time-integration method. The computational domain is truncated by a perfectly matched layer (PML). We derive estimates for both the error due to reflections at the outer boundary of the PML, and due to discretizing the continuous PML equations. Using these estimates, we show how the … continued below

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page(s) pp. 19-46

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Sjogreen, B & Petersson, A July 26, 2004.

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We consider the two-dimensional Maxwell's equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary condition are discretized to second order accuracy employing an embedded technique which does not suffer from a ''small-cell'' time-step restriction in the explicit time-integration method. The computational domain is truncated by a perfectly matched layer (PML). We derive estimates for both the error due to reflections at the outer boundary of the PML, and due to discretizing the continuous PML equations. Using these estimates, we show how the parameters of the PML can be chosen to make the discrete solution of the PML equations converge to the solution of Maxwell's equations on the unbounded domain, as the grid size goes to zero. Several numerical examples are given.

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page(s) pp. 19-46

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  • Journal Name: Journal of Computational Physics; Journal Volume: 209; Other Information: Journal publication date May 10, 2005; PDF-FILE: 38 ; SIZE: 2 MBYTES

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  • Report No.: UCRL-JRNL-205595
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 15016551
  • Archival Resource Key: ark:/67531/metadc1407608

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  • July 26, 2004

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  • Jan. 23, 2019, 12:54 p.m.

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  • Feb. 8, 2019, 3:38 p.m.

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Sjogreen, B & Petersson, A. Perfectly matched layers for Maxwell's equations in second order formulation, article, July 26, 2004; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc1407608/: accessed May 14, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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