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- W2319975304 abstract "This article is dedicated to the computation of the moments of the solution to elliptic partial differential equations with random, log-normally distributed diffusion coefficients by the quasi-Monte Carlo method. Our main result is that the convergence rate of the quasi-Monte Carlo method based on the Halton sequence for the moment computation depends only linearly on the dimensionality of the stochastic input parameters. In particular, we attain this rather mild dependence on the stochastic dimensionality without any randomization of the quasi-Monte Carlo method under consideration. For the proof of the main result, we require related regularity estimates for the solution and its powers. These estimates are also provided here. Numerical experiments are given to validate the theoretical findings." @default.
- W2319975304 created "2016-06-24" @default.
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- W2319975304 date "2016-03-24" @default.
- W2319975304 modified "2023-10-18" @default.
- W2319975304 title "On the quasi-Monte Carlo method with Halton points for elliptic PDEs with log-normal diffusion" @default.
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- W2319975304 doi "https://doi.org/10.1090/mcom/3107" @default.
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