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Foundations of Computational Mathematics
Erschienen in: Foundations of Computational Mathematics 6/2016

01.12.2016

Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation

verfasst von: Frances Y. Kuo, Dirk Nuyens

Erschienen in: Foundations of Computational Mathematics | Ausgabe 6/2016

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Abstract

This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers and contrasts the uniform case versus the lognormal case, single-level algorithms versus multi-level algorithms, first-order QMC rules versus higher-order QMC rules, and deterministic QMC methods versus randomized QMC methods. It gives a summary of the error analysis and proof techniques in a unified view, and provides a practical guide to the software for constructing and generating QMC points tailored to the PDE problems. The analysis for the uniform case can be generalized to cover a range of affine parametric operator equations.
Vorheriger Artikel The Joy and Pain of Skew Symmetry
Nächster Artikel Do Orthogonal Polynomials Dream of Symmetric Curves?

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Metadaten
Titel
Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation
verfasst von
Frances Y. Kuo
Dirk Nuyens
Publikationsdatum
01.12.2016
Verlag
Springer US
Erschienen in
Foundations of Computational Mathematics / Ausgabe 6/2016
Print ISSN: 1615-3375
Elektronische ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-016-9329-5

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