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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presence of a high-dimensional stochastic parameter space withdiscontinuities poses major computational challenges in analyzing andquantifying the effects of the uncertainties in a physical system. In thispaper, we propose a stochastic collocation method with adaptive mesh refinement(SCAMR) to deal with high dimensional stochastic systems with discontinuities.Specifically, the proposed approach uses generalized polynomial chaos (gPC)expansion with Legendre polynomial basis and solves for the gPC coefficientsusing the least squares method. It also implements an adaptive mesh (element)refinement strategy which checks for abrupt variations in the output based onthe second order gPC approximation error to track discontinuities ornon-smoothness. In addition, the proposed method involves a criterion forchecking possible dimensionality reduction and consequently, the decompositionof the full-dimensional problem to a number of lower-dimensional subproblems.Specifically, this criterion checks all the existing interactions between inputdimensions of a specific problem based on the high-dimensional modelrepresentation (HDMR) method, and therefore automatically provides thesubproblems which only involve interacting dimensions. The efficiency of theapproach is demonstrated using both smooth and non-smooth function exampleswith input dimensions up to 300, and the approach is compared against otherexisting algorithms.

Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis