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

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageAmerican English
Article number5464326
Pages (from-to)1439-1449
Number of pages11
JournalIEEE Transactions on Plasma Science
Issue number6 PART 1
StatePublished - 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: [email protected]). S. J. Cooke, A. N. Vlasov, and B. Levush are with the U.S. Naval Research Laboratory, Washington, DC 20375 USA (e-mail: [email protected]; [email protected]; [email protected]). 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: [email protected]). I. A. Chernyavskiy is with SAIC, McLean, VA 22102 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier 10.1109/TPS.2010.2047274


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


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