Isogeometric analysis of diffusion problems on random surfaces

Abstract: In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest may be derived. In particular, we employ a low rank approximation algorithm for the high-dimensional space-time correlation of the random solution based on an online singular value decomposition, cp. [7]. Extensive numerical studies are performed to validate the approach. In particular, we consider complex computational geometries originating from surface triangulations. The latter can be recast into the isogeometric context by transforming them into quadrangulations using the procedure from [41] and a subsequent approximation by NURBS surfaces.