Random Interior Data Representations in Probabilistic Boundary Element Anallysis

Abstract

Stochastic boundary element formulations have been recently developed for analyzing boundary value problems described by differential equations with random operators [1,2]. The domain excitations in these formulations were treated using the particular integral approach [3] wherein random properties at locations within the domain were expressed in terms of their values on the boundary only. The response on the boundary was independent of the variation of random properties inside the domain, and that at an internal point was affected by the random properties at that location only. A careful examination of the corresponding integral representations reveals that, in general, response statistics for locations on both the contour and within the domain, may depend on random properties of the entire object.