Name
Title | ||
|---|---|---|
A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields. |
Abstract | ||
|---|---|---|
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen-Loeve (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving a mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1082688 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
multilevel methods,PDEs with random input data,mixed finite elements,uncertainty quantification,multilevel Monte Carlo | Mathematical optimization,Monte Carlo method,Propagation of uncertainty,Random field,Finite element method,White noise,Gaussian,Sampling (statistics),Stochastic partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
39 | 5 | 1064-8275 |
Citations | PageRank | References |
1 | 0.35 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sarah Osborn | 1 | 2 | 1.07 |
| Panayot S. Vassilevski | 2 | 500 | 118.98 |
| Umberto Villa | 3 | 30 | 6.64 |