Advertisement

Simulation of Microwave and Semiconductor Laser Structures Including Absorbing Boundary Conditions

  • Georg Hebermehl
  • Friedrich Karl Hübner
  • Rainer Schlundt
  • Thorsten Tischler
  • Horst Zscheile
  • Wolfgang Heinrich
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 35)

Abstract

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 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

Keywords

Eigenvalue Problem Transmission Line Linear Algebraic Equation Krylov Subspace Perfectly Match Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Beilenhoff, K., Heinrich, W., Hartnagel, H. L.: Improved Finite-Difference Formulation in Frequency Domain for Three-Dimensional Scattering Problems. IEEE Transactions on Microwave Theory and Techniques 40 (1992) 540–546CrossRefGoogle Scholar
  2. 2.
    Christ, A., Hartnagel, H. L.: Three-Dimensional Finite-Difference Method for the Analysis of Microwave-Device Embedding. IEEE Transactions on Microwave Theory and Techniques 35 (1987) 688–696CrossRefGoogle Scholar
  3. 3.
    Bronstein, I. N., Semendjajew, K.A.: Taschenbuch der Mathematik. B. G. Teubner Verlagsgesellschaft (1965)Google Scholar
  4. 4.
    Davis, T. A., Duff, I. S.: A Combined Unifrontal/Multifrontal Method for Un-symmetric Sparse Matrices. University of Florida, Technical Report 16 (1997) 1–18Google Scholar
  5. 5.
    Eisenstat, S. C.: Efficient implementation of a class of preconditioned conjugate gradient methods. SIAM J. Sci Statist. Comput. 2 (1981) 1–4MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Freund, R. W., Malhotra, W.: A Block-QMR Algorithm for Non-Hermitian Linear Systems with Multiple Right-Hand Sides. Linear Algebra and Its Applications, 254 (1997) 119–157MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hebermehl, G., Schlundt, R., Zscheile, H., Heinrich W.: Improved Numerical Methods for the Simulation of Microwave Circuits, Surveys on Mathematics for Industry, 9 (1999) 117–129zbMATHGoogle Scholar
  8. 8.
    Hebermehl, G., Hübner, F.-K., Schlundt, R., Tischler, T., Zscheile, H., Heinrich, W.: On the Computation of Eigen Modes for Lossy Microwave Transmission Lines Including Perfectly Matched Layer Boundary Conditions. The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 20 (2001) 948–964CrossRefzbMATHGoogle Scholar
  9. 9.
    Hebermehl, G., Hübner, F.-K., Schlundt, R., Tischler, T., Zscheile, H., Heinrich, W.: Numerical Simulation of Lossy Microwave Transmission Lines Including PML. In: Scientific Computing in Electrical Engineering (ed. U. van Rienen, M. Günther, D. Hecht), Lecture Notes in Computational Science and Engineering, Springer Verlag, (2001) 267–275CrossRefGoogle Scholar
  10. 10.
    Lehoucq, R. B.: Analysis and Implementation of an Implicitly Restarted Arnoldi Iteration. Rice University, Department of Computational and Applied Mathematics, Technical Report 13 (1995) 1–135Google Scholar
  11. 11.
    März, R.: Integrated Optics - Design and Modeling. Artech House, (1995)Google Scholar
  12. 12.
    Saad, Y.: Iterative methods for sparse linear systems. PWS Publishing Company (1996)Google Scholar
  13. 13.
    Sacks, Z. S., Kingsland, D. M., Lee, R., Lee, J.-F.: A Perfectly Matched Anisotropic Absorber for Use as an Absorbing Boundary Condition. IEEE Transactions on Antennas and Propagation 43 (1995) 1460–1463CrossRefGoogle Scholar
  14. 14.
    Schenk, O., Gärtner, K., Fichtner, W.: Efficient Sparse LU Factorization with Left-Right Looking Strategy on Shared Memory Multiprocessors. BIT 40 (2000) 158–176MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Schenk, O., Gärtner, K.: Two-Level Dynamic Scheduling in PARDISO: Improved Scalability on Shared Memory Multiprocessing Systems. Parallel Computing 28 (2002) 187–197CrossRefzbMATHGoogle Scholar
  16. 16.
    Schlundt, R., Hebermehl, G., Hübner, F.-K., Heinrich, W., Zscheile, H.: Iterative Solution of Systems of Linear Equations in Microwave Circuits Using a Block Quasi-Minimal Residual Algorithm. In: Scientific Computing in Electrical Engineering (ed. U. van Rienen, M. Günther, D. Hecht), Lecture Notes in Computational Science and Engineering, Springer Verlag, (2001) 325–333CrossRefGoogle Scholar
  17. 17.
    Sorensen, D. C.: Implicit Application of Polynomial Filters in a k-Step Arnoldi Method. SIAM J. Matr. Anal. Apps. 13 (1992) 357–385MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis, Second Edition, Springer-Verlag (1993)zbMATHGoogle Scholar
  19. 19.
    Tischler, T., Heinrich, W.: The Perfectly Matched Layer as Lateral Boundary in Finite-Difference Transmission-Line Analsysis. IEEE Transactions on Microwave Theory and Techniques 48 (2000) 2249–2253CrossRefGoogle Scholar
  20. 20.
    Weiland, T.: A Discretization Method for the Solution of Maxwell’s Equations for Six-Component Fields. Electronics and Communication (AEU) 31 (1977) 116–120Google Scholar
  21. 21.
    Weiland, T.: On the Unique Numerical Solution of Maxwellian Eigenvalue Problems in Three Dimensions. Particle Accerelators 17 (1985) 227–242Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Georg Hebermehl
    • 1
  • Friedrich Karl Hübner
    • 1
  • Rainer Schlundt
    • 1
  • Thorsten Tischler
    • 2
  • Horst Zscheile
    • 2
  • Wolfgang Heinrich
    • 2
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Ferdinand-Braun-Institut für HöchstfrequenztechnikBerlinGermany

Personalised recommendations