WIAS Preprint No. 803, (2002)

Simulation of microwave and semiconductor laser structures including absorbing boundary conditions


  • Hebermehl, Georg
  • Hübner, Friedrich-Karl
  • 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, PML boundary condition, Eigenvalue problem, Linear algebraic equations




The transmission properties of microwave and optical structures can be described in terms of their scattering matrix using a three-dimensional boundary value problem for Maxwell's equations. The computational domain is truncated by electric or magnetic walls, open structures are treated using the Perfectly Matched Layer (PML) Absorbing Boundary Condition. The boundary value problem is solved by a finite-volume scheme. This results in a two-step procedure: an eigenvalue problem for general complex matrices and the solution of a large-scale system of linear equations with indefinite symmetric complex matrices. The modes of smallest attenuation are located in a longsome region bounded by two parabolas, and are found solving a sequence of eigenvalue problems of modified matrices. To reduce the execution times a coarse and a fine grid, and two levels of parallelization can be used. For the computation of the discrete grid equations, advanced preconditioning techniques are applied to reduce the dimension and the number of iterations solving the large-scale systems of linear algebraic equations. These matrix problems need to be solved repeatedly for different right-hand sides, but with the same coefficient matrix. The used block quasi-minimal residual algorithm is a block Krylov subspace iterative method that incorporates deflation to delete linearly and almost linearly dependent vectors in the block Krylov sequences. Special attention is paid to the PML which causes significantly increased number of iterations within Krylov subspace methods.

Appeared in

  • Challenges in Scientific Computing - CISC 2002, Ed. E. Baensch, Lecture Notes in Computational Science and Engineering, Springer Verlag, Vol. 35, pp. 131--159, 2003

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