Name
Abstract | ||
|---|---|---|
We present a multi-index quasi Monte Carlo method for the solution of elliptic partial differential equations with random coefficients. By combining the multi-index sampling idea with randomly shifted rank-1 lattice rules, the algorithm constructs an estimator for the expected value of some functional of the solution. The efficiency of this new method is illustrated on a three-dimensional subsurface flow problem with lognormal diffusion coefficient with underlying Matern covariance function. This example is particularly challenging because of the small correlation length considered, and thus the large number of uncertainties that must be included. We show numerical evidence that it is possible to achieve a cost inversely proportional to the requested tolerance on the root-mean-square error, for problems with a smoothly varying random field. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1082561 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
multilevel Monte Carlo,multi-index Monte Carlo,quasi Monte Carlo,elliptic PDEs,uncertainty quantification | Rejection sampling,Monte Carlo method,Mathematical optimization,Random field,Monte Carlo algorithm,Hybrid Monte Carlo,Algorithm,Quasi-Monte Carlo method,Monte Carlo integration,Dynamic Monte Carlo method,Mathematics | Journal |
Volume | Issue | ISSN |
39 | 5 | 1064-8275 |
Citations | PageRank | References |
1 | 0.37 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pieterjan Robbe | 1 | 1 | 0.71 |
| Dirk Nuyens | 2 | 168 | 17.97 |
| Stefan Vandewalle | 3 | 501 | 62.63 |