Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Electrical, Control and Communication Engineering

The Journal of Riga Technical University

2 Issues per year

Open Access
See all formats and pricing
More options …

Finite Element Tearing and Interconnecting Method and its Algorithms for Parallel Solution of Magnetic Field Problems

Dániel Marcsa / Miklós Kuczmann
Published Online: 2013-09-05 | DOI: https://doi.org/10.2478/ecce-2013-0011


Because of the exponential increase of computational resource requirement for numerical field simulations of more and more complex physical phenomena and more and more complex large problems in science and engineering practice, parallel processing appears to be an essential tool to handle the resulting large-scale numerical problems. One way of parallelization of sequential (singleprocessor) finite element simulations is the use of domain decomposition methods. Domain decomposition methods (DDMs) for parallel solution of linear systems of equations are based on the partitioning of the analyzed domain into sub-domains which are calculated in parallel while doing appropriate data exchange between those sub-domains. In this case, the non-overlapping domain decomposition method is the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method. This paper describes one direct solver and two parallel solution algorithms of FETI method. Finally, comparative numerical tests demonstrate the differences in the parallel running performance of the solvers of FETI method. We use a single-phase transformer and a three-phase induction motor as twodimensional static magnetic field test problems to compare the solvers

Keywords : High performance computing; parallel processing; finite element analysis; magnetic fields

  • [1] M. Kuczmann, A. Iványi, The Finite Element Method in Magnetics. Budapest, Academic Press, 2008.Google Scholar

  • [2] J. Luomi, Finite Element Methods for Electrical Machines (lecture Notes for postgraduate course in electrical machines). Chalmers University of Technology, Göteborg, 1993.Google Scholar

  • [3] J. Kruis, Domain Decomposition Methods for Distributed Computing. Kippen, Stirling, Scotland, Saxe-Coburg Publication, 2006.Google Scholar

  • [4] C. Farhat, F. X. Roux, "A method of Finite Element Tearing and Interconnecting and its parallel solution algorithm", International Journal for Numerical Methods in Engineering, vol. 32, pp. 1205-1227, 1991.Web of ScienceGoogle Scholar

  • [5] D. J. Rixen, C. Farhat, R. Teuzar, J. Mandel, "Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparison with a direct sparse solver", International Journal for Numerical Methods in Engineering, vol 46, pp. 501-533, 1999.Google Scholar

  • [6] D. Marcsa, M. Kuczmann, "Comparison of domain decomposition methods for elliptic partial differential problems with unstructured meshes", Przeglad Elektrotechniczny, vol. 12b, pp. 1-4, 2012.Google Scholar

  • [7] Y. Saad, Iterative Methods for Sparse Linear Systems. 3rd edition, Philadelphia, PA, SIAM, 2003.Google Scholar

  • [8] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongara, V. Eijkhout, R. Pozo, C. Romine, H. V. der Vorst, Templates for the Solution of Linear Systems: Boulding Blocks for Iterative Methods. Philadelphia, PA, SIAM, 1994Google Scholar

  • [9] C. Farhat, K. Pierson, M. Lesionne, "The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems", Computer Methods in Applied Mechanics and Engineering, vol. 184, pp. 333-374, 2000.Google Scholar

  • [10] http://glaros.dtc.umn.edu/gkhome/views/metis. (Accessed November 27, 2012)Google Scholar

  • [11] C. Geuzaine, J.F. Remacle, "Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities", International Journal for Numerical Methods in Engineering, vol. 79, pp. 1309-1331, 2009.Web of ScienceGoogle Scholar

  • [12] http://www.mathworks.com (Accessed November 20, 2012).Google Scholar

  • [13] P. Gosselet, C. Rey, D. J. Rixen, "On the initial estimate of interface forces in FETI methods", Computer Methods in Applied Mechanics and Engineering, vol. 192, pp. 2749-2764, 2003.Google Scholar

  • [14] F. Magoulés, F. X. Roux, "Algorithms and theory for substructuring and domain decomposition methods'', in Mesh Partitioning Techniques and Domain Decomposition Methods, F. Magoulés, Eds, Kippen, Stirling, Scotland: Saxe-Coburg Publications, 2007, pp. 89-118.Google Scholar

  • [15] H. Kanayama, S.-I. Sugimoto, ''Effectiveness of A-φ method in a parallel computing with an iterative domain decomposition method'', IEEE Transactions on Magnetics, vol. 42, pp. 539-542, 2006.Google Scholar

  • [16] Y. Fragakis, M. Papadrakakis, "The mosaic of high performance domain decomposition methods for structural mechanics: formulation, interrelation and numerical efficiency of primal and dual methods", Computer Methods in Applied Mechanics and Engineering, vol. 192, pp. 3799-3830, 2003.Google Scholar

  • [17] N. Bianchi, Electrical Machine Analysis Using Finite Elements, Taylor & Francis, Boca Rotan, FL, USA, 2005.Google Scholar

  • [18] A. F. P. Camargos, R. M. S. Batalha, C. A. P. S. Martins, E.J. Silva, G. L. Soares, ''Superlinear speedup in a 3-D parallel conjugate gradient solver'', IEEE Transactions on Magnetics, vol. 45, pp. 1602-1605, 2009.Web of ScienceGoogle Scholar

About the article

Dániel Marcsa

Dániel Marcsa was born in Keszthely, 8th of August, 1984, in Hungary. He has become B.Sc. in Electrical Engineering in 2008, and M.Sc. in Mechatronics Enginnering in 2010 at the Széchenyi Istvan University. He is recently a Ph.D. student at the Széchenyi István University, Győr, Hungary. His research is on static magnetic and eddy current potential formulations, numerical simulation of the electric machines by finite element method, and non-overlapping domain decomposition techniques in electromagnetic computation. He is an active member of the Laboratory of Electromagnetic Field and Hungarian Electrotechnical Association, and member of IEEE and International COMPUMAG Society. He received the Best Presenter Award at the 6th International PhD & DLA Symposium in 2010. Postal address: Széchenyi István University, Department of Automation, H-9026, Győr, Egyetem tér 1., Hungary.

Miklós Kuczmann

Miklós Kuczmann was born in Kapuvár, 31st of May, 1977, in Hungary. He has become M.Sc. in Electrical Engineering in 2000, and Ph.D. in Electrical Engineering in 2005 at the Budapest University of Technology and Economics, Department of Electromagnetic Theory. He is presently the head of the Department of Automation, Széchenyi István University, Győr, Hungary, where he is full professor since 2012. Dr. Kuczmann has won the Bolyai János Scholarship from the Hungarian Academy of Sciences in 2006, and the “Best PhD Dissertation” award in 2006 from the same Institute. Postal address: Széchenyi István University, Department of Automation, H-9026, Győr, Egyetem tér 1., Hungary.

Published Online: 2013-09-05

Published in Print: 2013-08-01

Citation Information: Electrical, Control and Communication Engineering, Volume 3, Issue 1, Pages 25–30, ISSN (Online) 2255-9159, ISSN (Print) 2255-9140, DOI: https://doi.org/10.2478/ecce-2013-0011.

Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in