Compact 3-D envelope ADI-FDTD algorithm for simulations of coherent radiation sources

Mordechai Botton; Simon J. Cooke; Thomas M. Antonsen; Igor A. Chernyavskiym; Alexander N. Vlasov; Baruch Levush

doi:10.1109/TPS.2010.2047274

Compact 3-D envelope ADI-FDTD algorithm for simulations of coherent radiation sources

Mordechai Botton^*, Simon J. Cooke, Thomas M. Antonsen, Igor A. Chernyavskiym, Alexander N. Vlasov, Baruch Levush

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A modified complex-envelope (CE) alternatingdirection-implicit (ADI) finite-difference time-domain solver for electromagnetic (EM) fields is presented. Like the conventional ADI scheme, the modified scheme is based on splitting the time step into two halves. In each substep, Maxwell's equations are solved implicitly in one direction and explicitly in the perpendicular direction. The new scheme is a combination of the conventional CE-ADI scheme and the leapfrog ADI scheme that was recently reported. The main features are a more compact form of the tridiagonal equations and greater flexibility in the application of boundary conditions. The boundary conditions on the six faces of the solution box are general and can be specified either as perfect conductor, symmetry boundary conditions, cavity modes, or arbitrary external specification. The new compact CE-ADI scheme is unconditionally stable; thus, the time step can be larger than the one imposed by the Courant-Friedrichs-Lewy (CFL) condition. Fast stable EM simulations of a planar slow-wave structure are demonstrated, with time steps exceeding the CFL limit by two orders of magnitude.

Original language	American English
Article number	5464326
Pages (from-to)	1439-1449
Number of pages	11
Journal	IEEE Transactions on Plasma Science
Volume	38
Issue number	6 PART 1
DOIs	https://doi.org/10.1109/TPS.2010.2047274
State	Published - Jun 2010

Bibliographical note

Funding Information:
Manuscript received October 15, 2009; revised January 11, 2010; accepted February 19, 2010. Date of publication May 17, 2010; date of current version June 9, 2010. This work was supported by the U.S. Office of Naval Research. M. Botton is with the Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: bdmoti@phys.huji.ac.il). S. J. Cooke, A. N. Vlasov, and B. Levush are with the U.S. Naval Research Laboratory, Washington, DC 20375 USA (e-mail: simon.cooke@nrl.navy.mil; vlasov@ccs.nrl.navy.mil; baruch.levush@nrl.navy.mil). T. M. Antonsen, Jr., is with Science Applications International Corporation (SAIC), McLean, VA 22102 USA, and also with the Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742-3511 USA (e-mail: antonsen@glue.umd.edu). I. A. Chernyavskiy is with SAIC, McLean, VA 22102 USA (e-mail: igor.a.chernyavskiy@saic.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2010.2047274

Keywords

Alternating direction implicit (ADI)
Slow-wave structure
Vacuum electronics

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10.1109/TPS.2010.2047274

Cite this

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title = "Compact 3-D envelope ADI-FDTD algorithm for simulations of coherent radiation sources",

abstract = "A modified complex-envelope (CE) alternatingdirection-implicit (ADI) finite-difference time-domain solver for electromagnetic (EM) fields is presented. Like the conventional ADI scheme, the modified scheme is based on splitting the time step into two halves. In each substep, Maxwell's equations are solved implicitly in one direction and explicitly in the perpendicular direction. The new scheme is a combination of the conventional CE-ADI scheme and the leapfrog ADI scheme that was recently reported. The main features are a more compact form of the tridiagonal equations and greater flexibility in the application of boundary conditions. The boundary conditions on the six faces of the solution box are general and can be specified either as perfect conductor, symmetry boundary conditions, cavity modes, or arbitrary external specification. The new compact CE-ADI scheme is unconditionally stable; thus, the time step can be larger than the one imposed by the Courant-Friedrichs-Lewy (CFL) condition. Fast stable EM simulations of a planar slow-wave structure are demonstrated, with time steps exceeding the CFL limit by two orders of magnitude.",

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author = "Mordechai Botton and Cooke, {Simon J.} and Antonsen, {Thomas M.} and Chernyavskiym, {Igor A.} and Vlasov, {Alexander N.} and Baruch Levush",

note = "Funding Information: Manuscript received October 15, 2009; revised January 11, 2010; accepted February 19, 2010. Date of publication May 17, 2010; date of current version June 9, 2010. This work was supported by the U.S. Office of Naval Research. M. Botton is with the Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: bdmoti@phys.huji.ac.il). S. J. Cooke, A. N. Vlasov, and B. Levush are with the U.S. Naval Research Laboratory, Washington, DC 20375 USA (e-mail: simon.cooke@nrl.navy.mil; vlasov@ccs.nrl.navy.mil; baruch.levush@nrl.navy.mil). T. M. Antonsen, Jr., is with Science Applications International Corporation (SAIC), McLean, VA 22102 USA, and also with the Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742-3511 USA (e-mail: antonsen@glue.umd.edu). I. A. Chernyavskiy is with SAIC, McLean, VA 22102 USA (e-mail: igor.a.chernyavskiy@saic.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2010.2047274",

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AU - Chernyavskiym, Igor A.

AU - Vlasov, Alexander N.

AU - Levush, Baruch

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N2 - A modified complex-envelope (CE) alternatingdirection-implicit (ADI) finite-difference time-domain solver for electromagnetic (EM) fields is presented. Like the conventional ADI scheme, the modified scheme is based on splitting the time step into two halves. In each substep, Maxwell's equations are solved implicitly in one direction and explicitly in the perpendicular direction. The new scheme is a combination of the conventional CE-ADI scheme and the leapfrog ADI scheme that was recently reported. The main features are a more compact form of the tridiagonal equations and greater flexibility in the application of boundary conditions. The boundary conditions on the six faces of the solution box are general and can be specified either as perfect conductor, symmetry boundary conditions, cavity modes, or arbitrary external specification. The new compact CE-ADI scheme is unconditionally stable; thus, the time step can be larger than the one imposed by the Courant-Friedrichs-Lewy (CFL) condition. Fast stable EM simulations of a planar slow-wave structure are demonstrated, with time steps exceeding the CFL limit by two orders of magnitude.

AB - A modified complex-envelope (CE) alternatingdirection-implicit (ADI) finite-difference time-domain solver for electromagnetic (EM) fields is presented. Like the conventional ADI scheme, the modified scheme is based on splitting the time step into two halves. In each substep, Maxwell's equations are solved implicitly in one direction and explicitly in the perpendicular direction. The new scheme is a combination of the conventional CE-ADI scheme and the leapfrog ADI scheme that was recently reported. The main features are a more compact form of the tridiagonal equations and greater flexibility in the application of boundary conditions. The boundary conditions on the six faces of the solution box are general and can be specified either as perfect conductor, symmetry boundary conditions, cavity modes, or arbitrary external specification. The new compact CE-ADI scheme is unconditionally stable; thus, the time step can be larger than the one imposed by the Courant-Friedrichs-Lewy (CFL) condition. Fast stable EM simulations of a planar slow-wave structure are demonstrated, with time steps exceeding the CFL limit by two orders of magnitude.

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Compact 3-D envelope ADI-FDTD algorithm for simulations of coherent radiation sources

Abstract

Bibliographical note

Keywords

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