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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

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MINIMAL SPARSE SAMPLING FOR FOURIER-POLYNOMIAL CHAOS IN ACOUSTIC SCATTERING

Volume 5, Issue 1, 2015, pp. 1-20
DOI: 10.1615/Int.J.UncertaintyQuantification.2015010084
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ABSTRACT

Single frequency acoustic scattering from an uncertain surface (with sinusoidal components) admits an efficient Fourier-polynomial chaos (FPC) expansion of the acoustic field. The expansion coefficients are computed non-intrusively, i.e., by functional sampling from existing acoustic models. The structure of the acoustic decomposition permits sparse selection of FPC orders within the framework of the Smolyak construction. The main result shows a minimal, sparse sampling required to exactly reconstruct FPC expansions of Smolyak form. To this end, this paper defines two concepts: exactly discretizable orthonormal, function systems (EDO); and nested systems created by decimation or "fledging". An EDO generalizes the Nyquist-Shannon sampling conditions (exact recovery of "band-limited" functions given sufficient sampling) to multidimensional FPC expansions. EDO criteria replace the concept of polynomially exact quadrature. Fledging parallels the idea of sub-sampling for sub-bands, from higher to lower level. The FPC Smolyak construction is an EDO fledged from a full grid EDO. An EDO results exactly when the sampled FPC expansion can be inverted to find its coefficients. EDO fledging requires that the lower level (1) has grid points and expansion orders nested in the higher level, and (2) derives its map from the samples to the coefficients from the higher level map. The theory begins with a single dimension fledged EDO, since a tensor product of fledged EDOs yields a fledged tensor EDO. A sequence of nested EDO levels fledge recursively from the largest EDO. The Smolyak construction uses telescoping sums of tensor products up to a maximum level to develop nested EDO systems for sparse grids and orders. The Smolyak construction transform gives exactly the inverse of the weighted evaluation map, and that inverse has a condition number that expresses the numerical limitations of the Smolyak construction.

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