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Monte Carlo Simulation of Dynamical Systems of Engineering Interest in a Massively Parallel Computing Environment: an Application of Genetic Algorithms

  • Erik A. Johnson
  • Lawrence A. Bergman
  • David E. Goldberg
  • Shirley J. Dyke
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)

Abstract

The evolution of a stochastic dynamical system is governed by a Fokker-Planck equation if its response process is Markovian. An analytical solution for nonstationary response does not exist for any but the simplest systems of engineering interest. The evolution of the transition probability density function over the phase space has been solved numerically for various two- and three-state systems subjected to additive and multiplicative white noise excitation using the finite element method [27,28]. Systems of higher order, however, can pose significant difficulty when using standard finite element formulations due to memory requirements and computational expense, leading to the use of various economization measures, a discussion of which lies beyond the scope of this paper.

Keywords

Genetic Algorithm Monte Carlo Simulation Direct Monte Carlo Simulation Duffing Oscillator Stochastic Dynamical System 
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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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Erik A. Johnson
    • 1
  • Lawrence A. Bergman
    • 1
  • David E. Goldberg
    • 2
  • Shirley J. Dyke
    • 3
  1. 1.Department of Aeronautical and Astronautical EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of General EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Department of Civil Engineering and Geological SciencesUniversity of Notre DameNotre DameUSA

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