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International Journal for Uncertainty Quantification

Published 6 issues per year

ISSN Print: 2152-5080

ISSN Online: 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

Indexed in

BLOCK AND MULTILEVEL PRECONDITIONING FOR STOCHASTIC GALERKIN PROBLEMS WITH LOGNORMALLY DISTRIBUTED PARAMETERS AND TENSOR PRODUCT POLYNOMIALS

Volume 7, Issue 5, 2017, pp. 441-462
DOI: 10.1615/Int.J.UncertaintyQuantification.2017020377
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ABSTRACT

The stochastic Galerkin method is a popular numerical method for solution of differential equations with randomly distributed data. We focus on isotropic elliptic problems with lognormally distributed coefficients. We study the block-diagonal preconditioning and the algebraic multilevel preconditioning based on the block splitting according to some hierarchy of approximation spaces for the stochastic part of the solution. We introduce upper bounds for the resulting condition numbers, and we derive a tool for obtaining sharp guaranteed upper bounds for the strengthened Cauchy-Bunyakovsky-Schwarz constant, which can serve as an indicator of the efficiency of some of these preconditioning methods. The presented multilevel approach yields a tool for efficient guaranteed two-sided a posteriori estimates of algebraic errors and for adaptive algorithms as well.

CITED BY
  1. Hrnčíř Jakub, Pultarová Ivana, Strakoš Zdeněk, Decomposition into subspaces preconditioning: abstract framework, Numerical Algorithms, 83, 1, 2020. Crossref

  2. Čertíková Marta, Gaynutdinova Liya, Pultarová Ivana, Multilevel a posteriori error estimator for greedy reduced basis algorithms, SN Applied Sciences, 2, 4, 2020. Crossref

  3. Kubínová Marie, Pultarová Ivana, Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds, SIAM/ASA Journal on Uncertainty Quantification, 8, 1, 2020. Crossref

  4. Petrov Miroslav S., Todorov Todor D., Properties of the multidimensional finite elements, Applied Mathematics and Computation, 391, 2021. Crossref

  5. Bespalov Alex, Loghin Daniel, Youngnoi Rawin, Truncation Preconditioners for Stochastic Galerkin Finite Element Discretizations, SIAM Journal on Scientific Computing, 43, 5, 2021. Crossref

  6. Pultarová Ivana, Ladecký Martin, Two‐sided guaranteed bounds to individual eigenvalues of preconditioned finite element and finite difference problems, Numerical Linear Algebra with Applications, 28, 5, 2021. Crossref

  7. Plešinger Martin, Pultarová Ivana, On the extreme eigenvalues of certain matrices of non-standard inner products of Hermite polynomials, Linear Algebra and its Applications, 546, 2018. Crossref

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