Analysis and computation of the elastic wave equation with random coefficients

Mohammad Motamed, Fabio Nobile, Raul Tempone

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given quantities of interest. We study the convergence rate of the error in the stochastic collocation method. In particular, we show that, the rate of convergence depends on the regularity of the solution or the quantity of interest in the stochastic space, which is in turn related to the regularity of the deterministic data in the physical space and the type of the quantity of interest. We demonstrate that a fast rate of convergence is possible in two cases: for the elastic wave solutions with high regular data; and for some high regular quantities of interest even in the presence of low regular data. We perform numerical examples, including a simplified earthquake, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo sampling method for approximating quantities with high stochastic regularity.
Original languageEnglish (US)
Pages (from-to)2454-2473
Number of pages20
JournalComputers & Mathematics with Applications
Volume70
Issue number10
DOIs
StatePublished - Oct 21 2015

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