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Local polynomial chaos expansion met...
~
Chen, Yi.
Local polynomial chaos expansion method for high dimensional stochastic differential equations.
紀錄類型:
書目-語言資料,手稿 : Monograph/item
正題名/作者:
Local polynomial chaos expansion method for high dimensional stochastic differential equations./
作者:
Chen, Yi.
面頁冊數:
1 online resource (101 pages)
附註:
Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:
Dissertation Abstracts International78-05B(E).
標題:
Applied mathematics. -
電子資源:
click for full text (PQDT)
ISBN:
9781369245998
Local polynomial chaos expansion method for high dimensional stochastic differential equations.
Chen, Yi.
Local polynomial chaos expansion method for high dimensional stochastic differential equations.
- 1 online resource (101 pages)
Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Thesis (Ph.D.)
Includes bibliographical references
Polynomial chaos expansion is a widely adopted method to determine evolution of uncertainty in dynamical system with probabilistic uncertainties in parameters. In particular, we focus on linear stochastic problems with high dimensional random inputs. Most of the existing methods enjoyed the efficiency brought by PC expansion compared to sampling-based Monte Carlo experiments, but still suffered from relatively high simulation cost when facing high dimensional random inputs. We propose a localized polynomial chaos expansion method that employs a domain decomposition technique to approximate the stochastic solution locally. In a relatively lower dimensional random space, we are able to solve subdomain problems individually within the accuracy restrictions. Sampling processes are delayed to the last step of the coupling of local solutions to help reduce computational cost in linear systems. We perform a further theoretical analysis on combining a domain decomposition technique with a numerical strategy of epistemic uncertainty to approximate the stochastic solution locally. An establishment is made between Schur complement in traditional domain decomposition setting and the local PCE method at the coupling stage. A further branch of discussion on the topic of decoupling strategy is presented at the end to propose some of the intuitive possibilities of future work. Both the general mathematical framework of the methodology and a collection of numerical examples are presented to demonstrate the validity and efficiency of the method.
Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018
Mode of access: World Wide Web
ISBN: 9781369245998Subjects--Topical Terms:
1069907
Applied mathematics.
Index Terms--Genre/Form:
554714
Electronic books.
Local polynomial chaos expansion method for high dimensional stochastic differential equations.
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Polynomial chaos expansion is a widely adopted method to determine evolution of uncertainty in dynamical system with probabilistic uncertainties in parameters. In particular, we focus on linear stochastic problems with high dimensional random inputs. Most of the existing methods enjoyed the efficiency brought by PC expansion compared to sampling-based Monte Carlo experiments, but still suffered from relatively high simulation cost when facing high dimensional random inputs. We propose a localized polynomial chaos expansion method that employs a domain decomposition technique to approximate the stochastic solution locally. In a relatively lower dimensional random space, we are able to solve subdomain problems individually within the accuracy restrictions. Sampling processes are delayed to the last step of the coupling of local solutions to help reduce computational cost in linear systems. We perform a further theoretical analysis on combining a domain decomposition technique with a numerical strategy of epistemic uncertainty to approximate the stochastic solution locally. An establishment is made between Schur complement in traditional domain decomposition setting and the local PCE method at the coupling stage. A further branch of discussion on the topic of decoupling strategy is presented at the end to propose some of the intuitive possibilities of future work. Both the general mathematical framework of the methodology and a collection of numerical examples are presented to demonstrate the validity and efficiency of the method.
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