Perfectly matched layer for the time domain finite element method

Thomas Rylander, Jian Ming Jin

Research output: Contribution to journalArticlepeer-review


A new perfectly matched layer (PML) formulation for the time domain finite element method is described and tested for Maxwell's equations. In particular, we focus on the time integration scheme which is based on Galerkin's method with a temporally piecewise linear expansion of the electric field. The time stepping scheme is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form, which reduces to the well-known Newmark scheme in the case without PML. Extensive numerical tests on scattering from infinitely long metal cylinders in two dimensions show good accuracy and no signs of instabilities. For a circular cylinder, the proposed scheme indicates the expected second order convergence toward the analytic solution and gives less than 2% root-mean-square error in the bistatic radar cross section (RCS) for resolutions with more than 10 points per wavelength. An ogival cylinder, which has sharp corners supporting field singularities, shows similar accuracy in the monostatic RCS.

Original languageEnglish (US)
Pages (from-to)238-250
Number of pages13
JournalJournal of Computational Physics
Issue number1
StatePublished - Oct 10 2004


  • Dispersive material
  • Perfectly matched layer
  • Time domain finite element method
  • Time integration

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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