Show simple item record

dc.contributor.authorKouri, D.P.
Heinkenschloss, M.
Ridzal, D.
van Bloemen Waanders, B.G.
dc.date.accessioned 2016-02-02T19:17:44Z
dc.date.available 2016-02-02T19:17:44Z
dc.date.issued 2013
dc.identifier.citation Kouri, D.P., Heinkenschloss, M., Ridzal, D., et al.. "A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty." SIAM Journal on Scientific Computing, 35, no. 4 (2013) SIAM: A1847-A1879. http://dx.doi.org/10.1137/120892362.
dc.identifier.urihttps://hdl.handle.net/1911/88307
dc.description.abstract The numerical solution of optimization problems governed by partial differential equations (PDEs) with random coefficients is computationally challenging because of the large number of deterministic PDE solves required at each optimization iteration. This paper introduces an efficient algorithm for solving such problems based on a combination of adaptive sparse-grid collocation for the discretization of the PDE in the stochastic space and a trust-region framework for optimization and fidelity management of the stochastic discretization. The overall algorithm adapts the collocation points based on the progress of the optimization algorithm and the impact of the random variables on the solution of the optimization problem. It frequently uses few collocation points initially and increases the number of collocation points only as necessary, thereby keeping the number of deterministic PDE solves low while guaranteeing convergence. Currently an error indicator is used to estimate gradient errors due to adaptive stochastic collocation. The algorithm is applied to three examples, and the numerical results demonstrate a significant reduction in the total number of PDE solves required to obtain an optimal solution when compared with a Newton conjugate gradient algorithm applied to a fixed high-fidelity discretization of the optimization problem.
dc.language.iso eng
dc.publisher SIAM
dc.rights Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.title A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
dc.type Journal article
dc.contributor.funder Air Force Office of Scientific Research
dc.contributor.funder National Science Foundation
dc.contributor.funder U.S. Department of Energy, Office of Advanced Scientific Computing Research, Office of Science
dc.contributor.funder NNSA Advanced Scientific Computing program
dc.citation.journalTitle SIAM Journal on Scientific Computing
dc.subject.keywordPDE optimization
uncertainty
stochastic collocation
trust regions
sparse grids
adaptivity
dc.citation.volumeNumber 35
dc.citation.issueNumber 4
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1137/120892362
dc.identifier.grantID FA9550-09-1-0225 (Air Force Office of Scientific Research)
dc.identifier.grantID DMS-0915238 (National Science Foundation)
dc.identifier.grantID DE-AC02-06CH11357 (U.S. Department of Energy, Office of Advanced Scientific Computing Research, Office of Science)
dc.type.publication publisher version
dc.citation.firstpage A1847
dc.citation.lastpage A1879


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record