Skip to main content

Fast and Efficient Methods for Circuit-based Automotive EMC Simulation

  • Conference paper
Time Domain Methods in Electrodynamics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 121))

Abstract

This paper presents a novel approach to eliminate the most serious bottlenecks in BEM-based EMC simulation by introducing fast and efficient modeling and solving techniques. A suitable modeling of 3D electromagnetic effects by an equivalent circuit representation can be accomplished by the well-established PEEC method. Typically, the resulting system matrices can be very large, dense and ill-conditioned. To enable the analysis of real-life problems, an acceleration has to be applied to the modeling as well as the solving process. Within the scope of this work, a methodology was developed to realize an overall EMC simulation process with significantly reduced complexity in terms of CPU time and storage demands for the underlying equation system. Various methods for model extraction and solving were investigated, including Hierarchical matrices (ℋ-matrices) and the well-known Algebraic multigrid (AMG) approach, allowing simulations with almost optimal complexity, in principle. These methods fulfill the accuracy demands and are suitable for parallel implementation. The generality, robustness, flexibility and efficiency of the proposed methods are shown by means of numerical results from a typical automotive application.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. E. Ruehli, “Equivalent Circuit Models for Three-Dimensional Multiconductor Systems,” IEEE Trans. Microw. Theory Tech., vol. MTT-22, no. 3, pp. 216–221, March 1974.

    Google Scholar 

  2. H. Heeb and A. E. Ruehli, “Retarded Models for PC Board Interconnects - or How the Speed of Light Affects Your SPICE Circuit Simulation,” in Proc. of the IEEE International Conference on Computer-Aided Design, November 1991, pp. 70–73.

    Google Scholar 

  3. R. F. Harrington, Field Computation by Moment Methods. Macmillan Publishing Company, 1968, reprint: IEEE Press, New York, 1993.

    Google Scholar 

  4. J. Ekman, “Electromagnetic Modeling Using the Partial Element Equivalent Circuit Method,” Ph.D. dissertation, Luleå University of Technology, Luleå, Sweden, 2003.

    Google Scholar 

  5. A. Görisch and G. Wollenberg, “Simulation von PEEC Modellen mit SPICE,” in Proc. of the EMV, Düsseldorf, Germany, 2000, pp. 181–188, (In German).

    Google Scholar 

  6. A. E. Ruehli, G. Antonini, J. Esch, J. Ekman, A. Orlandi, and A. Mayo, “Nonorthogonal PEEC Formulation for Time- and Frequency Domain EM and Circuit Modeling,” IEEE Trans. Electromagn. Compat., vol. 45, no. 2, pp. 167–176, 2003.

    Google Scholar 

  7. M. L. Zitzmann, “Fast and Efficient Methods for Circuit-based Automotive EMC Simulation,” Ph.D. dissertation, University of Erlangen-Nuremberg, Germany, 2007.

    Google Scholar 

  8. T.-H. Chen, C. Luk, and C. C.-P. Chen, “INDUCTWISE: Inductance-Wise Interconnect Simulator and Extractor,” IEEE Trans. Computer-Aided Design, vol. 22, no. 7, pp. 884–894, July 2003.

    Google Scholar 

  9. J. Vlach and K. Singhal, Computer-Methods for Circuit Analysis and Design, 2nd ed. Van Nostrand Reinhold, New York, 1994.

    Google Scholar 

  10. M. E. Verbeek, “Iterative Solvers and Preconditioning for Electromagnetic Boundary Integral Equations,” Ph.D. dissertation, University of Utrecht, Netherlands, 2001.

    Google Scholar 

  11. G. Antonini, “Fast Multipole Method for Time Domain PEEC Analysis,” IEEE Trans. Mobile Comput., vol. 2, no. 4, pp. 275–287, October-December 2003.

    Google Scholar 

  12. G. Antonini and A. E. Ruehli, “Fast Multiple and Multifunction PEEC Methods,” IEEE Trans. Mobile Comput., vol. 2, no. 4, pp. 288–298, October-December 2003.

    Google Scholar 

  13. S. Börm and S. A. Sauter, “Classical BEM with Linear Complexity,” MathComp., vol. 74, pp. 1139–1177, 2005.

    MATH  Google Scholar 

  14. M. Lintner, “Lösung der 2D Wellengleichung mittels hierarchischer Matrizen,” Ph.D. dissertation, Technical University of Munich, Germany, 2002, (In German).

    Google Scholar 

  15. L. Grasedyk, “Adaptive Recompression of ℋ-Matrices for BEM,” Computing, vol. 74, pp. 205–223, 2004.

    Article  Google Scholar 

  16. M. Bebendorf and R. Kriemann, “Fast Parallel Solution of Boundary Integral Equations and Related Problems,” Max Planck Institute for Mathematics in the Sciences, preprint 10/2004. [Online]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

  17. W. Hackbusch, “A Sparse Matrix arithmetic Based on ℋ-Matrices. Part I: Introduction to ℋ-Matrices,” Computing, vol. 62, pp. 89–108, 1999. [Online]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

  18. W. Hackbusch, “A Sparse ℋ-Matrix Arithmetic, Part II: Application to Multi-Dimensional Problems,” Computing, vol. 64, pp. 21–47, 2000. [Online]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

  19. S. Börm, “Approximation of Integral Operators by ℋ2-Matrices with Adaptive Bases,” Computing, vol. 74, pp. 249–271, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Bebendorf, “Project Homepage”. [Online]. Available: url: http://www.math.uni-leipzig.de/ bebendorf/projekte.html

    Google Scholar 

  21. U. Langer and D. Pusch, “Sparse Algebraic Multigrid Methods for Large Scale Boundary Element Equations,” Johannes Kepler University of Linz, Austria, 2003, Special Research Program SFB F013.

    Google Scholar 

  22. M. Bebendorf, “Approximation of Boundary Element Matrices,” Numer. Math., vol. 86, no. 4, pp. 565–589, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  23. L. Banjai and W. Hackbusch, “ℋ- and ℋ2-Matrices for Low and High Frequency Helmholtz Equation,” Max Planck Institute for Mathematics in the Sciences, preprint 17/2005. [Online]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

  24. S. Börm and L. Grasedyk, “Hybrid Cross Approximation of Integral Operators,” Max Planck Institute for Mathematics in the Sciences, preprint 68/2004. [On-line]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

  25. M. Bebendorf, “Approximate Inverse Preconditioning of FE Systems for Elliptic Operators with non-smooth Coefficients,” Max Planck Institute for Mathematics in the Sciences, preprint 7/2004. [Online]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

  26. W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. ARTECH House Norwood, MA 2001.

    Google Scholar 

  27. W. Hackbusch, “Multi-Grid Methods for FEM and BEM Applications,” Max Planck Institute for Mathematics in the Sciences, preprint 72, 2003. [Online]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

  28. D. Pusch, “Efficient Algebraic Multigrid Preconditioners for Boundary Element Methods,” Master’s thesis, Johannes Kepler University of Linz, Austria, 2003.

    Google Scholar 

  29. T. Clees, “AMG Strategies for PDE Systems with Applications in Industrial Semiconductor Simulation,” Ph.D. dissertation, University of Köln, Germany, 2005.

    Google Scholar 

  30. M. Bollhöfer, “Geometrische Mehrgitterverfahren und Algebraische Mehrgitterverfahren - Eine Einführung,” Lecture notes, Technical University of Berlin, Germany, 2001, (In German).

    Google Scholar 

  31. V. E. Henson, “An Algebraic Multigrid Tutorial,” Center of Applied Scientific Computing, Lawrence Livermore National Laboratory Livermore, CA, 1999.

    Google Scholar 

  32. H. Su, E. Acar, and S. R. Nassif, “Power Grid Reduction Based on Algebraic Multigrid Principles,” in Proc. of the International Design Automation Conference, Anaheim, CA, USA, June 2003.

    Google Scholar 

  33. S. R. Nassif and J. N. Kozhaya, “Fast Power Grid Simulation,” in Proc. of the International Design Automation Conference, Los Angeles, CA, USA, June 2000.

    Google Scholar 

  34. R. Beals, “Exact Fundamental Solutions,” Journées Équations aux dérivées partielles, June 1998.

    Google Scholar 

  35. A. Schüller, K. Stüben, C.-A. Thole, and U. Trottenberg, “Paralleles Rechnen und schnelle Simulation,” Der GMD-Spiegel, no. 1/2, pp. 9–11, 2000, (In German).

    Google Scholar 

  36. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Publishing Company Boston, MA, 1996.

    MATH  Google Scholar 

  37. K. Stüben and T. Clees, SAMG User’s Manual v. 22c, Fraunhofer Institute SCAI, Schloss Birlinghoven, Sankt Augustin, Germany, May 2005. [Online]. Available: url: http://www.scai.fhg.de/303.0.html

    Google Scholar 

  38. K. Stüben, SAMG - Data Structure and File Format Specification, Fraunhofer Institute SCAI, Sankt Augustin, Germany, February 2005.

    Google Scholar 

  39. A. Krechel and K. Stüben, “GMD Report 71: Parallel Algebraic Multigrid Based on Subdomain Blocking,” GMD - Forschungszentrum Informationstechnik GmbH, Germany, Tech. Rep., 1999.

    Google Scholar 

  40. The MISEA Project. [Online]. Available: url: http://misea.de

    Google Scholar 

  41. M. L. Zitzmann, T. Clees, and R. Weigel, “Iterative Methods for Reluctance based PEEC Models,” in Proc. of the 17th International Zurich Symposium on Electromagnetic Compatibility, Singapore 2006, February 27th - March 3rd, 2006, pp. 81–84.

    Google Scholar 

  42. A. Devgan, H. Ji, and W. Dai, “How to Efficiently Capture On-Chip Inductance Effects: Introducing a New Circuit Element K,” in Proc. of the International Conference on Computer-Aided Design, November 2000, pp. 150–155.

    Google Scholar 

  43. H. Zheng, B. Krauter, M. Beattie, and L. Pileggi, “Window-Based Susceptance Models for Large-Scale RLC Circuit Analyses,” in Proc. of the International Conference on Design, Automation and Test in Europe, 2002, pp. 628–633.

    Google Scholar 

  44. F. Canavero, J.-C. Kedzia, P. Ravier, and B. Scholl, “Numerical Simulation for Early EMC Design of Cars,” in Proc. of the CEM 2000 Symposium, Brugge, Belgium, 2000.

    Google Scholar 

  45. S. Börm and L. Grasedyk, “Hlib – A Library for ℋ- and ℋ2-matrices,” Max Planck Institute for Mathematics in the Sciences. [Online]. Available: url: http://www.hlib.org/

    Google Scholar 

  46. M. L. Zitzmann, R. Grillmair, T. Clees, and R. Weigel, “Hybrid Solver Strategies in Automotive EMC Simulation,” in Proc. of the 17th International Zurich Symposium on Electromagnetic Compatibility, Singapore 2006, February 27th - March 3rd, 2006, pp. 340–343.

    Google Scholar 

  47. T. Clees, T. Samrowski, M. L. Zitzmann, and R. Weigel, “An Automatic Multi-Level Solver Switching Strategy for PEEC-Based EMC Simulation,” in Proc. of the 18th International Zurich Symposium on Electromagnetic Compatibility, Munich 2007, (accepted).

    Google Scholar 

  48. J. Ekman and G. Antonini, “On Characterizing Artifacts Observed in PEEC Based Modeling,” in Proc. of the IEEE International Symposium on Electromagnetic Compatibility, Santa Clara, CA, USA, August 2004.

    Google Scholar 

  49. R. Achar and M. S. Nakhla, “Simulation of High-Speed Interconnects,” Proc. IEEE, vol. 89, no. 5, pp. 693–728, May 2001.

    Google Scholar 

  50. J. H. Bramble, Z. Leyk, and J. E. Pasciak, “The Analysis of Multigrid Algorithms for Pseudo-Differential Operators of Order Minus One,” Math. Comp., vol. 63, no. 208, pp. 461–478, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  51. K. Stüben and T. Clees, SAMG User’s Manual v. 22c, Fraunhofer Institute SCAI, Schloss Birlinghoven, Sankt Augustin, Germany, May 2005. [Online]. Available: url: http://www.scai.fhg.de/303.0.html

    Google Scholar 

  52. R. Kriemann, “Parallel ℋ-Matrix Arithmetics on Shared Memory Systems,” Max Planck Institute for Mathematics in the Sciences, preprint 29/2004. [Online]. Available: url: http://www.mis.mpg.de/preprints/

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zitzmann, M.L., Weigel, R. (2008). Fast and Efficient Methods for Circuit-based Automotive EMC Simulation. In: Russer, P., Siart, U. (eds) Time Domain Methods in Electrodynamics. Springer Proceedings in Physics, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68768-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68768-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68766-5

  • Online ISBN: 978-3-540-68768-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics