Name
Title | ||
|---|---|---|
Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs. |
Abstract | ||
|---|---|---|
In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. The local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained from the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In this paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140970100 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
generalized polynomial chaos,domain decomposition,stochastic differential equation,uncertainty quantification | Mathematical optimization,Stochastic optimization,Uncertainty quantification,Mathematical analysis,Linear differential equation,Stochastic differential equation,Polynomial chaos,Stochastic partial differential equation,Partial differential equation,Domain decomposition methods,Mathematics | Journal |
Volume | Issue | ISSN |
37 | 1 | 1064-8275 |
Citations | PageRank | References |
5 | 0.72 | 14 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yi Chen | 1 | 5 | 0.72 |
| John D. Jakeman | 2 | 52 | 7.65 |
| Claude Jeffrey Gittelson | 3 | 24 | 3.58 |
| Dongbin Xiu | 4 | 1068 | 115.57 |