Research Article

A FETI-DP method for the parallel iterative solution of indefinite and complex-valued solid and shell vibration problems

  1. Charbel Farhat1,*,
  2. Jing Li2,
  3. Philip Avery1

Article first published online: 21 FEB 2005

DOI: 10.1002/nme.1282

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 63, Issue 3, pages 398–427, 21 May 2005

Additional Information

How to Cite

Farhat, C., Li, J. and Avery, P. (2005), A FETI-DP method for the parallel iterative solution of indefinite and complex-valued solid and shell vibration problems. International Journal for Numerical Methods in Engineering, 63: 398–427. doi: 10.1002/nme.1282

Author Information

  1. 1

    Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Building 500, Stanford, CA 94305-3035, U.S.A.

  2. 2

    Department of Mathematical Sciences, Kent State University, Kent, OH 44242, U.S.A.

*Department of Aerospace Engineering Sciences and Center for Aerospace Structures, University of Colorado, Campus Box 429, Boulder, CO 80309-0429, U.S.A.

Publication History

  1. Issue published online: 31 MAR 2005
  2. Article first published online: 21 FEB 2005
  3. Manuscript Accepted: 3 NOV 2004
  4. Manuscript Revised: 27 AUG 2004
  5. Manuscript Received: 7 JUL 2004

Funded by

  • The Sandia National Laboratories. Grant Numbers: 31095, 29341
  • The National Science Foundation. Grant Number: DMS-0209297

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Keywords:

  • FETI-DP;
  • FETI-DPH;
  • domain decomposition;
  • PCG;
  • PGMRES;
  • indefinite;
  • complex

Abstract

The dual-primal finite element tearing and interconnecting (FETI-DP) domain decomposition method (DDM) is extended to address the iterative solution of a class of indefinite problems of the form (K−σ2M)u=f, and a class of complex problems of the form (K−σ2M+iσD)u=f, where K, M, and D are three real symmetric matrices arising from the finite element discretization of solid and shell dynamic problems, i is the imaginary complex number, and σ is a real positive number. A key component of this extension is a new coarse problem based on the free-space solutions of Navier's equations of motion. These solutions are waves, and therefore the resulting DDM is reminiscent of the FETI-H method. For this reason, it is named here the FETI-DPH method. For a practically large σ range, FETI-DPH is shown numerically to be scalable with respect to all of the problem size, substructure size, and number of substructures. The CPU performance of this iterative solver is illustrated on a 40-processor computing system with the parallel solution, for various σ ranges, of several large-scale, indefinite, or complex-valued systems of equations associated with shifted eigenvalue and forced frequency response structural dynamics problems. Copyright © 2005 John Wiley & Sons, Ltd.

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