English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In many models used in engineering and science, material properties areuncertain or spatially varying. For example, in geophysics, and porous mediaflow in particular, the uncertain permeability of the material is modelled as arandom field. These random fields can be highly anisotropic. Efficient solvers,such as the Multiple Semi-Coarsened Multigrid (MSG) method, see [15, 16, 17],are required to compute solutions for various realisations of the uncertainmaterial. The MSG method is an extension of the classic Multigrid method, thatuses additional coarse grids that are coarsened in only a single coordinatedirection. In this sense, it closely resembles the extension of MultilevelMonte Carlo (MLMC) [6] to Multi-Index Monte Carlo (MIMC) [9]. We present anunbiased MIMC method that reuses the MSG coarse solutions, similar to the workin [11]. Our formulation of the estimator can be interpreted as the problem oflearning the unknown distribution of the number of samples across all indices,and unifies the previous work on adaptive MIMC [19] and unbiased estimation[18]. We analyse the cost of this new estimator theoretically and presentnumerical experiments with various anisotropic random fields, where the unknowncoefficients in the covariance model are considered as hyperparameters. Weillustrate its robustness and superiority over unbiased MIMC without samplereuse.

Enhanced Multi-Index Monte Carlo by means of Multiple Semi-Coarsened Multigrid for Anisotropic Diffusion Problems