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dc.contributor.authorElman, Howard C.
dc.contributor.authorLiang, Jiaxing
dc.contributor.authorSánchez-Vizuet, Tonatiuh
dc.date.accessioned2024-02-09T20:10:03Z
dc.date.available2024-02-09T20:10:03Z
dc.date.issued2024-01-19
dc.identifier.citationElman, H. C., Liang, J., & Sánchez-Vizuet, T. (2024). Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem. Computer Physics Communications, 109099.en_US
dc.identifier.issn0010-4655
dc.identifier.doi10.1016/j.cpc.2024.109099
dc.identifier.urihttp://hdl.handle.net/10150/670933
dc.description.abstractThe equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.en_US
dc.description.sponsorshipU.S. Department of Energyen_US
dc.language.isoenen_US
dc.publisherElsevier BVen_US
dc.rights© 2024 Elsevier B.V. All rights reserved.en_US
dc.rights.urihttps://rightsstatements.org/vocab/InC/1.0/en_US
dc.subjectGeneral Physics and Astronomyen_US
dc.subjectHardware and Architectureen_US
dc.subjectAdaptive finite element discretizationen_US
dc.subjectFree boundary Grad-Shafranov problemen_US
dc.subjectMultilevel Monte Carlo Finite-Elementen_US
dc.subjectUncertainty quantificationen_US
dc.titleMultilevel Monte Carlo methods for the Grad-Shafranov free boundary problemen_US
dc.typeArticleen_US
dc.contributor.departmentDepartment of Mathematics, The University of Arizonaen_US
dc.identifier.journalComputer Physics Communicationsen_US
dc.description.note24 month embargo; first published 19 January 2024en_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal accepted manuscripten_US
dc.identifier.piiS0010465524000225
dc.source.journaltitleComputer Physics Communications
dc.source.volume298
dc.source.beginpage109099


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