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International Journal for Uncertainty Quantification
Главный редактор: Habib N. Najm (open in a new tab)
Ассоциированный редакторs: Dongbin Xiu (open in a new tab) Tao Zhou (open in a new tab)
Редактор-основатель: Nicholas Zabaras (open in a new tab)

Выходит 6 номеров в год

ISSN Печать: 2152-5080

ISSN Онлайн: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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A MULTIGRID MULTILEVEL MONTE CARLO METHOD USING HIGH-ORDER FINITE-VOLUME SCHEME FOR LOGNORMAL DIFFUSION PROBLEMS

Том 7, Выпуск 1, 2017, pp. 57-81
DOI: 10.1615/Int.J.UncertaintyQuantification.2016018677
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Краткое описание

The aim of this paper is to show that a high-order discretization can be used to improve the convergence of a multilevel Monte Carlo method for elliptic partial differential equations with lognormal random coefficients in combination with the multigrid solution method. To demonstrate this, we consider a fourth-order accurate finite-volume discretization. With the help of the Matérn family of covariance functions, we simulate the coefficient field with different degrees of smoothness. The idea behind using a fourth-order scheme is to capture the additional regularity in the solution introduced due to higher smoothness of the random field. Second-order schemes previously utilized for these types of problems are not able to fully exploit this additional regularity. We also propose a practical way of combining a full multigrid solver with the multilevel Monte Carlo estimator constructed on the same mesh hierarchy. Through this integration, one full multigrid solve at any level provides a valid sample for all the preceding Monte Carlo levels. The numerical results show that the fourth-order multilevel estimator consistently outperforms the second-order variant. In addition, we observe an asymptotic gain for the standard Monte Carlo estimator.

ЦИТИРОВАНО В
  1. Luo Peiyao, Rodrigo Carmen, Gaspar Francisco J., Oosterlee Cornelis W., Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System, SIAM Journal on Scientific Computing, 39, 5, 2017. Crossref

  2. Kumar Prashant, Luo Peiyao, Gaspar Francisco J., Oosterlee Cornelis W., A multigrid multilevel Monte Carlo method for transport in the Darcy–Stokes system, Journal of Computational Physics, 371, 2018. Crossref

  3. Robbe Pieterjan, Nuyens Dirk, Vandewalle Stefan, Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method, SIAM Journal on Scientific Computing, 41, 5, 2019. Crossref

  4. Herrmann Lukas, Strong convergence analysis of iterative solvers for random operator equations, Calcolo, 56, 4, 2019. Crossref

  5. Kumar Prashant, Schmelzer Martin, Dwight Richard P., Stochastic turbulence modeling in RANS simulations via multilevel Monte Carlo, Computers & Fluids, 201, 2020. Crossref

  6. Robbe Pieterjan, Nuyens Dirk, Vandewalle Stefan, Enhanced multi‐index Monte Carlo by means of multiple semicoarsened multigrid for anisotropic diffusion problems, Numerical Linear Algebra with Applications, 28, 3, 2021. Crossref

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