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In this article, we discuss the numerical solution of diffusion equations onrandom surfaces within the isogeometric framework. We describe in detail, howdiffusion problems on random surfaces can be modelled and how quantities ofinterest may be derived. In particular, we employ a low rank approximationalgorithm for the high-dimensional space-time correlation of the randomsolution based on an online singular value decomposition, cp. [7]. Extensivenumerical studies are performed to validate the approach. In particular, weconsider complex computational geometries originating from surfacetriangulations. The latter can be recast into the isogeometric context bytransforming them into quadrangulations using the procedure from [41] and asubsequent approximation by NURBS surfaces.

Isogeometric analysis of diffusion problems on random surfaces