Name
Title | ||
|---|---|---|
Variational Multiscale Analysis: The Fine-Scale Green's Function for Stochastic Partial Differential Equations |
Abstract | ||
|---|---|---|
We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating accurate coarse-scale solutions while accounting for the effect of the unresolved fine scales through a model term that contains a fine-scale stochastic Green's function. For a natural choice of an "optimal" coarse-scale solution and L-2-orthogonal stochastic basis functions, we demonstrate that the fine-scale stochastic Green's function is intimately linked to its deterministic counterpart. In particular, (i) we demonstrate that whenever the deterministic fine-scale function vanishes, the stochastic fine-scale function satisfies a weaker and discrete notion of vanishing stochastic coefficients, and (ii) we derive an explicit formula for the fine-scale stochastic Green's function that only involves quantities needed to evaluate the fine-scale deterministic Green's function. We present numerical results that support our claims about the physical support of the stochastic fine-scale function and demonstrate the benefit of using the VMS method when the fine-scale Green's function is approximated by an easier to implement element Green's function. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/130940359 | SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION |
Keywords | Field | DocType |
variational multiscale analysis,uncertainty quantification,stochastic partial differential equations | Applied mathematics,Stochastic optimization,Green's function,Uncertainty quantification,Mathematical analysis,Stochastic differential equation,Continuous-time stochastic process,Basis function,Stochastic partial differential equation,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
2 | 1 | 2166-2525 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| jayanth jagalurmohan | 1 | 0 | 0.34 |
| Onkar Sahni | 2 | 124 | 15.10 |
| Alireza Doostan | 3 | 188 | 15.57 |
| A. Oberai | 4 | 6 | 3.96 |