Physical Sciences and Mathematics Commons^™

Multilevel Hierarchical Decomposition Of Finite Element White Noise With Application To Multilevel Markov Chain Monte Carlo, Hillary R. Fairbanks, Umberto E. Villa, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable …