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Local polynomial chaos expansion method for high dimensional stochastic differential equations.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Local polynomial chaos expansion method for high dimensional stochastic differential equations./
Author:	Chen, Yi.
Description:	1 online resource (101 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
Subject:	Applied mathematics. -
Online resource:	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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035 $a AAI10170547
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099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Chen, Yi. $3 1180529
245 1 0 $a Local polynomial chaos expansion method for high dimensional stochastic differential equations.
264 0 $c 2016
300 $a 1 online resource (101 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Advisers: Dongbin Xiu; Suchuan Dong.
502 $a Thesis (Ph.D.) $c Purdue University $d 2016.
504 $a Includes bibliographical references
520 $a 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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Purdue University. $b Mathematics. $3 1180530
773 0 $t Dissertation Abstracts International $g 78-05B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10170547 $z click for full text (PQDT)