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ISSN 打印: 2152-5080

ISSN 在线: 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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AN ADAPTIVE REDUCED BASIS COLLOCATION METHOD BASED ON PCM ANOVA DECOMPOSITION FOR ANISOTROPIC STOCHASTIC PDES

卷 8, 册 3, 2018, pp. 193-210
DOI: 10.1615/Int.J.UncertaintyQuantification.2018024436
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摘要

The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parametrized partial differential equations (PDEs). In this paper, we study the stochastic collocation methods that can be combined with reduced basis methods to solve high-dimensional parametrized stochastic PDEs. We also propose an adaptive algorithm using a probabilistic collocation method (PCM) and ANOVA decomposition. This procedure involves two stages. First, the method employs an ANOVA decomposition to identify the effective dimensions, i.e., subspaces of the parameter space in which the contributions to the solution are larger, and sort the reduced basis solution in a descending order of error. Then, the adaptive search refines the parametric space by increasing the order of polynomials until the algorithm is terminated by a saturation constraint. We demonstrate the effectiveness of the proposed algorithm for solving a stationary stochastic convection-diffusion equation, a benchmark problem chosen because solutions contain steep boundary layers and anisotropic features. We show that two stages of adaptivity are critical in a benchmark problem with anisotropic stochasticity.

对本文的引用
  1. Liao Qifeng, Li Jinglai, An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems, Journal of Computational Physics, 396, 2019. Crossref

  2. Chen Chen, Liao Qifeng, ANOVA Gaussian process modeling for high-dimensional stochastic computational models, Journal of Computational Physics, 416, 2020. Crossref

  3. Williamson Kevin, Cho Heyrim, Sousedík Bedřich, Application of adaptive ANOVA and reduced basis methods to the stochastic Stokes-Brinkman problem, Computational Geosciences, 25, 3, 2021. Crossref

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