WIAS Preprint No. 620, (2000)

Iterative solution of systems of linear equations in microwave circuits using a block quasi-minimal residual algorithm


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

2010 Mathematics Subject Classification

  • 35Q60 65F10 65F15 65N22


  • Microwave device simulation, Scattering matrix, Maxwell's equations, Boundary value problem, Finite integration technique, Eigenvalue problem, System of linear algebraicequations, Multiple right-hand sides


The electric properties of monolithic microwave integrated circuits that are connected to transmission lines are described in terms of their scattering matrix using Maxwell's equations. Using a finite-volume method the corresponding three-dimensional boundary value problem of Maxwell's equations in the frequency domain can be solved by means of a two-step procedure. An eigenvalue problem for non-symmetric matrices yields the wave modes. The eigenfunctions determine the boundary values at the ports of the transmission lines for the calculation of the fields in the three-dimensional structure. The electromagnetic fields and the scattering matrix elements are achieved by the solution of large-scale systems of linear equations with indefinite complex symmetric coefficient matrices. In many situations, these matrix problems need to be solved repeatedly for different right-hand sides, but with the same coefficient matrix. The 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 underlying block Krylov sequences.

Appeared in

  • Lecture Notes in Computational Science and Engineering, Vol. 18 (2001), Eds. Ursula van Rienen, Michael Günther, Dirk Hecht: Scientific Computing in Electrical Engineering, pp. 325-333

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