Long-time performance of unsplit PMLs with explicit second order schemes

S. Abarbanel, H. Qasimov, S. Tsynkov

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


A gradual long-time growth of the solution in perfectly matched layers (PMLs) has been previously reported in the literature. This undesirable phenomenon may hamper the performance of the layer, which is designed to truncate the computational domain for unsteady wave propagation problems. For unsplit PMLs, prior studies have attributed the growth to the presence of multiple eigenvalues in the amplification matrix of the governing system of differential equations. In the current paper, we analyze the temporal behavior of unsplit PMLs for some commonly used second order explicit finite-difference schemes that approximate the Maxwell's equations. Our conclusion is that on top of having the PML as a potential source of long-time growth, the type of the layer and the choice of the scheme play a major role in how rapidly this growth may manifest itself and whether or not it manifests itself at all.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalJournal of Scientific Computing
Issue number1
StatePublished - Oct 2009
Externally publishedYes

Bibliographical note

Funding Information:
Research supported by the US Air Force, grant number FA9550-07-1-0170, and US NSF, grant number DMS-0509695.


  • Central difference/Runge-Kutta scheme
  • Lax-Wendroff scheme
  • Leap-frog scheme
  • Long-time growth
  • Maxwell's equations
  • Numerical solution
  • Perfectly matched layer (PML)
  • Second order approximation
  • Wave propagation
  • Yee scheme
  • Yee/Runge-Kutta scheme


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