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Conditioning analysis of separate displacement preconditioners for some nonlinear elasticity systems

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  • Axelsson, O.
  • Karátson, J.

Abstract

Separate displacement preconditioners are studied in the context of outer–inner iterations for a model in 3D nonlinear elasticity. Such a preconditioner, already known to be efficient for linear models, arises as the discretization of three independent Laplacian operators. In this paper the resulting condition number is investigated with focus on independence of parameters. Estimates are given which show that the condition number is uniformly bounded w.r.t. both the studied Newton iterate and the chosen discretization. Finally, it is sketched that ill-conditioning caused by nearly incompressible material parameters can be handled by a suitable mixed formulation.

Suggested Citation

  • Axelsson, O. & Karátson, J., 2004. "Conditioning analysis of separate displacement preconditioners for some nonlinear elasticity systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(6), pages 649-668.
  • Handle: RePEc:eee:matcom:v:64:y:2004:i:6:p:649-668
    DOI: 10.1016/j.matcom.2003.11.017
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    References listed on IDEAS

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    1. Georgiev, A & Margenov, S & Neytcheva, M, 1999. "Multilevel algorithms for 3D simulation of nonlinear elasticity problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(1), pages 175-182.
    2. Axelsson, Owe, 2003. "Iteration number for the conjugate gradient method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(3), pages 421-435.
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