Combining sparse grids, multilevel MC and QMC for elliptic PDEs with\n random coefficients

2017/11/07 by Michael B. Giles, Frances Y. Kuo, Giles, Michael B. +3
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1711.02437

openalex publication_date 2017/11/07 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Building on previous research which generalized multilevel Monte Carlo\nmethods using either sparse grids or Quasi-Monte Carlo methods, this paper\nconsiders the combination of all these ideas applied to elliptic PDEs with\nfinite-dimensional uncertainty in the coefficients. It shows the potential for\nthe computational cost to achieve an O(\ε) r.m.s. accuracy to be\nO(\ε^-r) with r<2, independently of the spatial dimension of the\nPDE.\n

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