WIAS Preprint No. 711, (2002)

Perfectly matched layers in transmission lines


  • Hebermehl, Georg
  • Hübner, Friedrich-Karl
  • Schlundt, Rainer
    ORCID: 0000-0002-4424-4301
  • Tischler, Thorsten
  • Zscheile, Horst
  • Heinrich, Wolfgang

2010 Mathematics Subject Classification

  • 35Q60 65F15 65N22


  • Microwave device, Optoelectronic device, Simulation, Maxwell's equation, PML boundary condition, Eigenvalue problem


The field distribution at the ports of the transmission line structure is computed by applying Maxwell's equations to the structure and solving an eigenvalue problem. The high dimensional sparse system matrix is complex in the presence of losses and Perfectly Matched Layer. A method is presented which preserves sparseness and delivers only the small number of interesting modes out with the smallest attenuation. The modes are found solving a sequence of eigenvalue problems of modified matrices with the aid of the invert mode of the Arnoldi iteration using shifts. A new strategy is described which allows the application of the method, first developed for microwave structures, to optoelectronic devices.

Appeared in

  • Numerical Mathematics and Advanced Applications, ENUMATH 2001, Springer Italia, Eds: Brezzi, F., Buffa, A., Corsaro, S., Murli, A., pp. 281-290

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