Numerical solution of one-dimensional wave equation with stochastic parameters using generalized polynomial chaos expansion

K. Sepahvand, S. Marburg, H. J. Hardtke

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

This paper presents a numerical algorithm which is using generalized polynomial chaos combined with the finite difference method for the solution of the one-dimensional wave equation with stochastic physical parameters. The stochastic parameters are represented by the Hermite polynomial chaos. A spectral-finite difference model for the numerical solution is introduced using generalized polynomial chaos expansion. The general conditions for convergence and stability of numerical algorithms are derived. Finally, the method is applied to a vibrating string. Results are compared with those of a Monte Carlo simulation.

Original languageEnglish
Pages (from-to)579-593
Number of pages15
JournalJournal of Computational Acoustics
Volume15
Issue number4
DOIs
StatePublished - Dec 2007
Externally publishedYes

Keywords

  • Polynomial chaos
  • Stochastic parameters
  • Uncertainty
  • Wave equation

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