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Boundary Element Analysis pp 281–352Cite as

BEM-Based Simulations in Engineering Design

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Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 29))

Abstract

The simulation of the real-world industrial problems is nowadays faced with a number of the challenging requirements, mainly arising in the daily design praxis of power engineering devices. Complex structures, complex physics, huge dimensions and huge aspect ratio in model dimensions are just some of the critical modelling issues that need to be encountered by the simulation tools. Thanks to the advances achieved in the last several years, BEM become a powerful numerical technique for the simulations of such industrial products. Until recent time this technique has been recognized as a technique offering from one side some excellent features (2D instead of 3D discretization, open-boundary problems, etc.), but from the other side having some serious practical limitations, mostly related to the full-populated, often ill-conditioned matrices. The new, emerging numerical techniques like MBIT (Multipole-Base Integral Technique), ACA (Adaptive Cross-Approximations), DDT (Domain-Decomposition Technique) seems to bridge some of these known bottlenecks, promoting those the BEM in a high-level tool for even daily-design process of the 3D real-world problems.

The aim of this Chapter is to illustrate how this numerical technique can be used for the simulation of both single-physics problems appearing in the Dielectric Design (Electrostatics), and multi-physics problems in Thermal Design (coupling of Electromagnetic-Heat Transfer) and Electro-Mechanical Design (coupling of Electromagnetic-Structural Mechanics) of power engineering devices like power transformers or switchgears.

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References

  1. Z. Andjelić, B. Krstajić, S. Milojković, Z. Haznadar: A Procedure for Automatic Optimal Shape Investigation of Interfaces Between Different Media. IEEE Trans. Mag. 24 (1988) 415–418.

    Article  Google Scholar 

  2. Z. Andjelić, E. Henrikson, O. Johendal, H. Nordman: 3D Simulation in Transformer Design. 10th Int. Sym. on High Voltage Engineering, Montreal, 1997.

    Google Scholar 

  3. Z. Andjelić, B. Krstajić, S. Milojković, A. Blaszczyk, H. Steinbigler, M. Wohlmuth: Integral Methods for the Calculation of Electric Fields. Scientific Series of the International Bureau, Vol. 10, Forschungszentrum Jülich GmbH, Germany, 1992.

    Google Scholar 

  4. Z. Andjelić, J. Ostrowski, B. Cranganu-Cretu: MBIT for Skin-effect Problems in Power Transformers. 4th European Congress on Computational Methods in Applied Sciences and Engineering-ECCOMAS, Jyväskylä, Finland, 2004.

    Google Scholar 

  5. Z. Andjelić, P. Marchukov: Acceleration of the Electrostatic Computation Using Multipole Technique. ABB internal report, Heidelberg, 1992.

    Google Scholar 

  6. Z. Andjelić, B. Krstajić, S. Milojković, S. Babić: Boundary Integral Method for Electromagnetic Field Computation. NSF project, Code JF824, USA, 1991.

    Google Scholar 

  7. B. A. Auld: Acoustic Fields and Waves in Solids, Vol. 1. John Wiley and Sons, New York, 1973.

    Google Scholar 

  8. S. Babić, Z. Andjelić, B. Krstajić, S. Salon: Analytical Magnetostatic Field Calculation for a Conductor with Uniform Current in the Longitudinal Direction. J. Appl. Phys. 67 (1990) 5827–5829.

    Article  Google Scholar 

  9. B. Bachmann: Freies Potential beim Ladungsverfahren. ETZ-A 94 (1973) 12.

    Google Scholar 

  10. P. K. Banerjee: The Boundary Element Methods in Engineering. McGraw-Hill Book Company, 1981.

    Google Scholar 

  11. M. Bebendorf, S. Rjasanow: Adaptive low rank approximation of collocation matrices. Computing 70 (2003) 1–24.

    Article  MATH  MathSciNet  Google Scholar 

  12. M. Bebendorf: Approximation of Boundary Element Matrices. Numer. Math 86 (2000) 565–589.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Bebendorf, S. Rjasanow, E. E. Tytyshnikov: Approximations using Diagonal-Plus Skeleton Matrices. In: Mathematical Aspects of Boundary Element Methods (M. Bonnet, A.-M. Sändig, W. L. Wendland eds.), Chapman & Hall/CRC Research Notes in Mathematics, Vol. 414, pp. 45–53, 1999.

    Google Scholar 

  14. M. Bebendorf: Hierarchical LU decomposition-based preconditioners for BEM. Computing 74 (2005) 225–247.

    Article  MATH  MathSciNet  Google Scholar 

  15. M. Bebendorf: Another software library on Hierarchical Matrices for elliptic differential equations (AHMED). Universität Leipzig, Fakultät für Mathematik und Informatik, 2005.

    Google Scholar 

  16. J. van Bladel: Singular Electromagnetic Fields and Sources. IEEE Press Series on Electromagnetic Wave Theory, 1995.

    Google Scholar 

  17. A. Blaszczyk, Z. Andjelić, P. Levin, A. Ustundag: Parallel Computation of Electric Fields in a Heterogeneous Workstation Cluster. In: HPCN Europe 95, Lecture Notes on Computer Science, Springer, Berlin, Heidelberg, pp. 606–611, 1995.

    Google Scholar 

  18. P. Bochev: On the Finite Element Solution of the Pure Neumann Problem. SIAM Review 47 (1992) 50–66.

    Article  MathSciNet  Google Scholar 

  19. H. Boehme: Mittelspannungstechnik. Verlag Technik GmbH, Berlin, München, 1992.

    Google Scholar 

  20. M. Costabel: Symmetric methods for the coupling of finite elements and boundary elements. In: Boundary Elements IX (C. A. Brebbia, G. Kuhn, W. L. Wendland eds.), Springer, Berlin, pp. 411–420, 1987.

    Google Scholar 

  21. E. Euxibie, J.-L. Coulomb, G. Meunier, J.-C. Sabonnadière: Mechanical deformation of a conductor under electromagnetic stresses. IEEE Trans. Mag. 22 (1986) 828–830.

    Article  Google Scholar 

  22. K. Fujiwara, T. Nakata: Results for Benchmark Problem 7, COMPEL 9 (1990) 137–154.

    Google Scholar 

  23. L. Gaul, M. Kögl, M. Wagner: Boundary Element Methods for Engineers and Scientists. Springer, Berlin, 2003.

    MATH  Google Scholar 

  24. L. Grasedyck, W. Hackbusch: Construction and Arithmetics of H-matrices. Computing 70 (2003) 295–334.

    Article  MATH  MathSciNet  Google Scholar 

  25. L. Greengard, V. Rokhlin: A Fast Algorithm for Particle Simulations. J. Comp. Phys. 73 (1987) 325–348.

    Article  MATH  MathSciNet  Google Scholar 

  26. G. H. Golub, C. F. van Loan: Matrix Computations. The Johns Hopkins University Press, Third edition, Baltimore, London, 1996.

    Google Scholar 

  27. W. Hackbusch, Z. P. Nowak: On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54 (1989) 463–491.

    Article  MATH  MathSciNet  Google Scholar 

  28. W. Hackbusch: The Panel Clustering Technique for the Boundary Element Method. 9th Int. Conf. on BEM, pp. 463–473, 1987.

    Google Scholar 

  29. H. A. Haus, J. R. Melcher: Electromagnetic Fields. MIT Publishing.

    Google Scholar 

  30. L. R. Hill, T. N. Farris: Three-Dimensional Piezoelectric Boundary Element Method. AIAA Journal 36, 1998.

    Google Scholar 

  31. R. Hiptmair: Coupled Boundary Element Scheme for Eddy Current Computation. 2nd Kolloquium Elektromagnetische Umformung, ETH Zürich, 2003.

    Google Scholar 

  32. Intel Math Kernel Library 8.0, Intel Software Development Product. http://www.intel.com/cd/software/products/asmo-na/eng/perflib/mkl

    Google Scholar 

  33. J. D. Jackson: Classical Electrodynamics. John Wiley, 1999.

    Google Scholar 

  34. A. B. Kemp, M. T. Grzegirczyk M., K. A. Kong: Ab inito study of the radiation pressure on dielectric and magnetic media. Optics Express 13 (2005).

    Google Scholar 

  35. E. C. Koleciskij: Rascet eletriceskih poljei ustroistv visokog naprezenija. Energoatomizdat, Moskva, 1983.

    Google Scholar 

  36. A. Kost: Numerische Methoden in der Berechnung elektromagnetischer Felder. Springer, 1994.

    Google Scholar 

  37. B. Krstajić, Z. Andjelić, S. Milojković, S. Babić: Nonlinear 3D Magnetostatic Field Calculation by the Integral Equation Method with Surface and Volume Magnetic Charges. IEEE Trans. Mag. 28 (1992).

    Google Scholar 

  38. C. Lage: Software development for Boundary Element Method: Analysis and design of efficient techniques. Ph.D. thesis, University of Kiel, Germany, 1995.

    Google Scholar 

  39. L. D. Landau, E. M. Lifshitz: Theory of Eleasticity. Pergamon Press, New York, 1959.

    Google Scholar 

  40. J. C. Maxwell: The Treatise on Electricity and Magnetism. Dover Publication, New York, 1954.

    Google Scholar 

  41. I. D. Mayergoyz: Boundary Integral Equations of Minimal Order for the Calculation of Three-Dimensional Eddy Current Problems. IEEE Trans. Mag. 18 (1982).

    Google Scholar 

  42. I. D. Mayergoyz: A New Approach to the Calculation of Three-Dimensional Skin Effect Problems. IEEE Trans. Mag. 19 (1983).

    Google Scholar 

  43. I. D. Mayergoyz: Nonlinear Magnetostatic Calculation Based on Fast Multipole Method. IEEE Trans. Mag. 39 (2003).

    Google Scholar 

  44. W. McLean: Strongly Eliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, UK, 2000.

    Google Scholar 

  45. J. R. Melcher: Continuum Electromechanics. MIT Press, Massachusetts, 1981

    Google Scholar 

  46. A. H. Nayfeh: Wave Propagation in Layered Anisotropic Media with Applications to Composites. Elsevier, Amsterdam, 1995.

    Google Scholar 

  47. S. Peaiyoung, S. J. Salon: Some Technial Aspects of Implementing Boundary Element Technique. IEEE Trans. Mag. 25 (1989).

    Google Scholar 

  48. G. Reyne, J. C. Sabonnadiere, J. L. Coulomb, P. Brissonneau: A Survay on the main aspects of magnetic forces and mechanical behaviour of ferromagnetic materials under magnetisation. IEEE Trans. Mag. 23 (1987).

    Google Scholar 

  49. A. H. Schatz, V. Thomée, W. L. Wendland: Mathematical Theory of Finite and Boundary Element Methods. Birkhäuser, Basel, 1990.

    MATH  Google Scholar 

  50. G. Schmidlin: Fast Solution Algorithms for Integral Equations in ℝ3. Ph.D. thesis, ETH Zürich, 2003.

    Google Scholar 

  51. G. Schmidlin, U. Fischer, Z. Andjelić, C. Schwab: Preconditioning of the second-kind boundary integral equations for 3D eddy current problems. Int. J. Numer. Meth. Engrg. 51 (2001) 1009–1031.

    Article  MATH  Google Scholar 

  52. K. R. Shao, K. D. Zhou, J. D. Lavwers: Boundary Element Analysis Method for 3-D Multiply Connected Eddy Current Problems Based on the Second Order Potential Formulation. IEEE Trans. Mag 28 (1992).

    Google Scholar 

  53. K. Simonyi: Theoretische Elektrotechnik. VEB Deutscher Verlag der Wissenschaften, Berlin, 1973.

    Google Scholar 

  54. S. Sirtori: General stress analysis method by means of integral equations and boundary elements. Meccanica 14 (1979) 210–218.

    Article  MATH  Google Scholar 

  55. J. Smajic, B. Cranganu-Cretu, J. Ostrowski, Z. Andjelić: Stationary Voltage and Current Excited Complex System of Multimaterial Conductors with BEM. IEEE Trans. Mag. (2006).

    Google Scholar 

  56. O. Steinbach: Numerische Näherungsverfahren für elliptische Randwertprobleme. B. G. Teubner, Stuttgart, 2003.

    Google Scholar 

  57. O. Steinbach: Lösungsverfahren für lineare Gleichungsysteme. Algoritmen und Anwendungen, B. G. Teubner, Wiesbaden, 2005.

    Google Scholar 

  58. O. Steinbach: OSTBEM. A Boundary Element Software Package, Universität Stuttgart, TU Graz, 1992–2006.

    Google Scholar 

  59. J. A. Stratton: Electromagnetic Theory. McGraw-Hill, 1941.

    Google Scholar 

  60. I. E. Tamm: Fundamentals of the Theory of Electricity. Mir Publisher, Moscow, 1965.

    Google Scholar 

  61. O. B. Tozoni, I. D. Maergoiz: Rascet trehmernih elektromagnetnih polei. Tehnika, Kiev, 1974.

    Google Scholar 

  62. J. Yuan, A. Kost: A Three-Component Boundary Element Algorithm for Three-Dimensional Eddy Current Calculation. IEEE Trans. Mag. 30 (1994).

    Google Scholar 

  63. L. Zehnder, J. Kiefer, D. Braun, T. Schoenemann: SF6 generator circuit-breaker system for short-circuit currents up to 200 kA, ABB Review 3, 2002.

    Google Scholar 

  64. J. R. Whiteman, L. Demkowicz: Mathematics of Finite Elements and Applications XI. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issues 2–5, 2005.

    Google Scholar 

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Authors and Affiliations

  1. Corporate Research, ABB Switzerland Ltd., 5405, Baden-Dättwil, Switzerland

    Zoran Andjelić, Jasmin Smajić & Michael Conry

Authors
  1. Zoran Andjelić
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  2. Jasmin Smajić
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  3. Michael Conry
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Editors and Affiliations

  1. Institut für Baumechanik, Technische Universität Graz, Technikerstr. 4, 8010, Graz, Austria

    Martin Schanz

  2. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Olaf Steinbach

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Andjelić, Z., Smajić, J., Conry, M. (2007). BEM-Based Simulations in Engineering Design. In: Schanz, M., Steinbach, O. (eds) Boundary Element Analysis. Lecture Notes in Applied and Computational Mechanics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47533-0_11

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  • DOI: https://doi.org/10.1007/978-3-540-47533-0_11

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  • Print ISBN: 978-3-540-47465-4

  • Online ISBN: 978-3-540-47533-0

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