WIAS Preprint No. 905, (2004)

Simulation of microwave circuits and laser structures including PML by means of FIT


  • Hebermehl, Georg
  • Schefter, Jürgen
  • Schlundt, Rainer
    ORCID: 0000-0002-4424-4301
  • Tischler, Thorsten
  • Zscheile, Horst
  • Heinrich, Wolfgang

2010 Mathematics Subject Classification

  • 35Q60 65N22 65F15 65F10


  • Microwave device, Semiconductor laser, Simulation, Maxwell's equations, Boundary value problem, PML boundarycondition, Eigenvalue problem, Linearalgebraic equations, Rectangular grids, Tetrahedral nets


Field-oriented methods which describe the physical properties of microwave circuits and optical structures are an indispensable tool to avoid costly and time-consuming redesign cycles. Commonly the electromagnetic characteristics of the structures are described by the scattering matrix which is extracted from the orthogonal decomposition of the electric field. The electric field is the solution of an eigenvalue and a boundary value problem for Maxwell's equations in the frequency domain. We discretize the equations with orthogonal grids using the Finite Integration Technique (FIT). Maxwellian grid equations are formulated for staggered nonequidistant rectangular grids and for tetrahedral nets with corresponding dual Voronoi cells. The interesting modes of smallest attenuation are found solving a sequence of eigenvalue problems of modified matrices. To reduce the execution time for high-dimensional problems a coarse and a fine grid is used. The calculations are carried out, using two levels of parallelization. The discretized boundary value problem, a large-scale system of linear algebraic equations with different right-hand sides, is solved by a block Krylov subspace method with various preconditioning techniques. Special attention is paid to the Perfectly Matched Layer boundary condition (PML) which causes non physical modes and a significantly increased number of iterations in the iterative methods.

Appeared in

  • Ädvances in Radio Science", vol. 2, pp. 107--112, (2004)

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