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＜電子ブック＞
Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs / by Dinh Dũng, Van Kien Nguyen, Christoph Schwab, Jakob Zech
(Lecture Notes in Mathematics. ISSN:16179692 ; 2334)

版	1st ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XV, 207 p : online resource
著者標目	*Dũng, Dinh author Nguyen, Van Kien author Schwab, Christoph author Zech, Jakob author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Probabilities LCSH:Numerical analysis LCSH:Functional analysis FREE:Differential Equations FREE:Probability Theory FREE:Numerical Analysis FREE:Functional Analysis
一般注記	The 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, suchas 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 HTTP:URL=https://doi.org/10.1007/978-3-031-38384-7

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