Research Article

Time-parallel implicit integrators for the near-real-time prediction of linear structural dynamic responses

  1. Charbel Farhat1,*,
  2. Julien Cortial1,
  3. Climène Dastillung2,
  4. Henri Bavestrello1

Article first published online: 31 JAN 2006

DOI: 10.1002/nme.1653

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 67, Issue 5, pages 697–724, 30 July 2006

Additional Information

How to Cite

Farhat, C., Cortial, J., Dastillung, C. and Bavestrello, H. (2006), Time-parallel implicit integrators for the near-real-time prediction of linear structural dynamic responses. Int. J. Numer. Meth. Engng., 67: 697–724. doi: 10.1002/nme.1653

Author Information

  1. 1

    Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305, U.S.A.

  2. 2

    Ecole Nationale des Ponts et Chaussées, France

*Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305, U.S.A.

Publication History

  1. Issue published online: 27 JUN 2006
  2. Article first published online: 31 JAN 2006
  3. Manuscript Accepted: 15 DEC 2005
  4. Manuscript Revised: 12 SEP 2005
  5. Manuscript Received: 23 OCT 2004

Funded by

  • National Science Foundation. Grant Number: 008463
  • Air Force Office of Scientific Research. Grant Number: F49620-01-1-0129

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Keywords:

  • PITA;
  • parallel time-integration;
  • real-time computing;
  • time-domain decomposition

Abstract

The time-parallel framework for constructing parallel implicit time-integration algorithms (PITA) is revisited in the specific context of linear structural dynamics and near-real-time computing. The concepts of decomposing the time-domain in time-slices whose boundaries define a coarse time-grid, generating iteratively seed values of the solution on this coarse time-grid, and using them to time-advance the solution in each time-slice with embarrassingly parallel time-integrations are maintained. However, the Newton-based corrections of the seed values, which so far have been computed in PITA and related approaches on the coarse time-grid, are eliminated to avoid artificial resonance and numerical instability. Instead, the jumps of the solution on the coarse time-grid are addressed by a projector which makes their propagation on the fine time-grid computationally feasible while avoiding artificial resonance and numerical instability. The new PITA framework is demonstrated for a complex structural dynamics problem from the aircraft industry. Its potential for near-real-time computing is also highlighted with the solution of a relatively small-scale problem on a Linux cluster system. Copyright © 2006 John Wiley & Sons, Ltd.

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