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Algebraic Multigrid for Solving Electromechanical Problems

  • Manfred Kaltenbacher
  • Stefan Reitzinger
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 14)

Abstract

In this work the simulation of electromechanical systems is considered. The numerical scheme, based on the Finite Element (FE) method, allows the simulation of coupled magnetic, mechanical and acoustic fields. Therefore an efficient, robust and fast solution strategy is required.

According to [3] a direct coupling between the mechanical and acoustic quantities and an iterative coupling within each time step between the mechanical and magnetic quantities are performed. Therewith, the mechanical-acoustic equation can be solved separately from the magnetic equation. Fortunately, in our applications the mechanical-acoustic part remains constant during the solution process. Thus a direct solver was taken and actually one factorization has to be performed. Since the motional ElectroMagnetic Force (EMF) term is taken into account by using a moving mesh technique, the magnetic part is a function of the mechanical displacement and therefore changes in each time step. Because the system matrix of the magnetic part is Symmetric Positive Definite (SPD) the Preconditioned Conjugate Gradient (PCG) with a preconditioner which is robust, fast and can be kept constant throughout some time steps is used. As a basis for a preconditioner we take Algebraic Multigrid (AMG) as introduced in [5]. In order to deal with non M-matrices we use the element preconditioning method (see [4]).

Numerical studies of the transient analysis of an electrodynamic loudspeaker are presented, showing the numerical robustness of the solution strategy.

Keywords

Multigrid Method Direct Solver Magnetic Part Symmetric Positive Definite Iterative Coupling 
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.

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References

  1. 1.
    Hackbusch, W.: Multigrid Methods and Applications, Springer Verlag, Berlin, Heidelberg, New York, 1985Google Scholar
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    Jung, M., Langer, U.: Applications of Multilevel Methods to Practical Problems, Surv. Math. Ind. 1 (1991), 217–257MathSciNetMATHGoogle Scholar
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    Kaltenbacher, M, Landes, H., Lerch, R.: An Efficient Calculation Scheme for the Numerical Simulation of Coupled Magnetomechanical Systems, IEEE Transactions on Magnetics 33 (1997), no. 2, 1646–1649CrossRefGoogle Scholar
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    Reitzinger, S., Algebraic Multigrid and Element Preconditioning, Technical SFB Report, Johannes Kepler Universität Linz, Institut für Mathematik, September 1999Google Scholar
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    Ruge, J.W., Stäben, K.: Algebraic Multigrid (AMG), Multigrid Methods (S. McCormick, ed.), Frontiers in Applied Mathematics, 5, SIAM, Philadelphia, 1986, 73–130Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Manfred Kaltenbacher
    • 1
  • Stefan Reitzinger
    • 2
  1. 1.Department of Sensor TechnologyUniversity of ErlangenErlangenGermany
  2. 2.Spezialforschungsbereich SFB F013 ‘Numerical and Symbolic Scientific Computing’University of LinzLinzAustria

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