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001482447 001__ 1482447
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001482447 019__ $$a1404016462$$a1404052459
001482447 020__ $$a9783031383847$$q(electronic bk.)
001482447 020__ $$a3031383842$$q(electronic bk.)
001482447 020__ $$z9783031383830
001482447 020__ $$z3031383834
001482447 0247_ $$a10.1007/978-3-031-38384-7$$2doi
001482447 035__ $$aSP(OCoLC)1404449130
001482447 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dOCLKB$$dYDX$$dEBLCP$$dYDX$$dOCLCO$$dOCLCF
001482447 049__ $$aISEA
001482447 050_4 $$aQA377$$b.D86 2023
001482447 08204 $$a515/.353$$223/eng/20231018
001482447 1001_ $$aDũng, Dinh,$$eauthor.$$0(orcid)0000-0003-2333-5623$$1https://orcid.org/0000-0003-2333-5623
001482447 24510 $$aAnalyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs /$$cDinh Dũng, Van Kien Nguyen, Christoph Schwab, Jakob Zech.
001482447 264_1 $$aCham, Switzerland :$$bSpringer,$$c2023.
001482447 300__ $$a1 online resource (xv, 207 pages).
001482447 336__ $$atext$$btxt$$2rdacontent
001482447 337__ $$acomputer$$bc$$2rdamedia
001482447 338__ $$aonline resource$$bcr$$2rdacarrier
001482447 4901_ $$aLecture notes in mathematics,$$x1617-9692 ;$$vvolume 2334
001482447 504__ $$aIncludes bibliographical references and index.
001482447 5050_ $$aIntro -- Preface -- Acknowledgement -- Contents -- List of Symbols -- List of Abbreviations -- 1 Introduction -- 1.1 An Example -- 1.2 Contributions -- 1.3 Scope of Results -- 1.4 Structure and Content of This Text -- 1.5 Notation and Conventions -- 2 Preliminaries -- 2.1 Finite Dimensional Gaussian Measures -- 2.1.1 Univariate Gaussian Measures -- 2.1.2 Multivariate Gaussian Measures -- 2.1.3 Hermite Polynomials -- 2.2 Gaussian Measures on Separable Locally Convex Spaces -- 2.2.1 Cylindrical Sets -- 2.2.2 Definition and Basic Properties of Gaussian Measures -- 2.3 Cameron-Martin Space
001482447 5058_ $$a2.4 Gaussian Product Measures -- 2.5 Gaussian Series -- 2.5.1 Some Abstract Results -- 2.5.2 Karhunen-Loève Expansion -- 2.5.3 Multiresolution Representations of GRFs -- 2.5.4 Periodic Continuation of a Stationary GRF -- 2.5.5 Sampling Stationary GRFs -- 2.6 Finite Element Discretization -- 2.6.1 Function Spaces -- 2.6.2 Finite Element Interpolation -- 3 Elliptic Divergence-Form PDEs with Log-Gaussian Coefficient -- 3.1 Statement of the Problem and Well-Posedness -- 3.2 Lipschitz Continuous Dependence -- 3.3 Regularity of the Solution -- 3.4 Random Input Data
001482447 5058_ $$a3.5 Parametric Deterministic Coefficient -- 3.5.1 Deterministic Countably Parametric Elliptic PDEs -- 3.5.2 Probabilistic Setting -- 3.5.3 Deterministic Complex-Parametric Elliptic PDEs -- 3.6 Analyticity and Sparsity -- 3.6.1 Parametric Holomorphy -- 3.6.2 Sparsity of Wiener-Hermite PC Expansion Coefficients -- 3.7 Parametric Hs(D)-Analyticity and Sparsity -- 3.7.1 Hs(D)-Analyticity -- 3.7.2 Sparsity of Wiener-Hermite PC Expansion Coefficients -- 3.8 Parametric Kondrat'ev Analyticity and Sparsity -- 3.8.1 Parametric Ks(D)-Analyticity
001482447 506__ $$aAccess limited to authorized users.
001482447 520__ $$aThe present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.
001482447 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 18, 2023).
001482447 650_6 $$aÉquations aux dérivées partielles.
001482447 650_6 $$aProcessus gaussiens.
001482447 650_6 $$aChamps aléatoires.
001482447 650_6 $$aAnalyse mathématique.
001482447 650_0 $$aDifferential equations, Partial.
001482447 650_0 $$aGaussian processes.
001482447 650_0 $$aRandom fields.
001482447 650_0 $$aMathematical analysis.$$xMathematical models$$0(DLC)sh2008104883
001482447 655_0 $$aElectronic books.
001482447 7001_ $$aNguyen, Van Kien,$$eauthor.
001482447 7001_ $$aSchwab, Ch.$$q(Christoph),$$eauthor.$$q(Christoph)$$0(OCoLC)oca04723370
001482447 7001_ $$aZech, Jakob,$$eauthor.
001482447 77608 $$iPrint version: $$z3031383834$$z9783031383830$$w(OCoLC)1385448228
001482447 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2334.$$x1617-9692
001482447 852__ $$bebk
001482447 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-38384-7$$zOnline Access$$91397441.1
001482447 909CO $$ooai:library.usi.edu:1482447$$pGLOBAL_SET
001482447 980__ $$aBIB
001482447 980__ $$aEBOOK
001482447 982__ $$aEbook
001482447 983__ $$aOnline
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