MATHICSE Technical Report : Analysis and computation of the elastic wave equation with random coefficients

We analyze 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 traditionalMonte Carlo sampling method for problems with high stochastic regularity.

Aug 23 2012
Écublens, MATHICSE
MATHICSE Technical Report Nr. 32.2012 August 2012
Related to:

 Record created 2019-01-21, last modified 2019-06-19

Version 1:
Download fulltext

Rate this document:

Rate this document:
(Not yet reviewed)