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This work describes a domain embedding technique between two non-matchingmeshes used for generating realizations of spatially correlated random fieldswith applications to large-scale sampling-based uncertainty quantification. Thegoal is to apply the multilevel Monte Carlo (MLMC) method for thequantification of output uncertainties of PDEs with random input coefficientson general, unstructured computational domains. We propose a highly scalable,hierarchical sampling method to generate realizations of a Gaussian randomfield on a given unstructured mesh by solving a reaction-diffusion PDE with astochastic right-hand side. The stochastic PDE is discretized using the mixedfinite element method on an embedded domain with a structured mesh, and thenthe solution is projected onto the unstructured mesh. This work describesimplementation details on how to efficiently transfer data from the structuredand unstructured meshes at coarse levels, assuming this can be done efficientlyon the finest level. We investigate the efficiency and parallel scalability ofthe technique for the scalable generation of Gaussian random fields in threedimensions. An application of the MLMC method is presented for quantifyinguncertainties of subsurface flow problems. We demonstrate the scalability ofthe sampling method with non-matching mesh embedding, coupled with a parallelforward model problem solver, for large-scale 3D MLMC simulations with up to$1.9\cdot 10^9$ unknowns.

Scalable hierarchical PDE sampler for generating spatially correlated random fields using non-matching meshes