Randomized sampling for basis function construction in generalized finite element methods


Journal Article

© 2020 Society for Industrial and Applied Mathematics. In the framework of generalized finite element methods for elliptic equations with rough coefficients, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several random sampling strategies that construct approximations to the optimal set of basis functions of a given dimension, and proposes a quantitative criterion to analyze and compare these sampling strategies. Numerical evidence shows that the best results are achieved by two strategies, Random Gaussian and Smooth Boundary sampling.

Full Text

Duke Authors

Cited Authors

  • Chen, K; Li, Q; Lu, J; Wright, SJ

Published Date

  • January 1, 2020

Published In

Volume / Issue

  • 18 / 2

Start / End Page

  • 1153 - 1177

Electronic International Standard Serial Number (EISSN)

  • 1540-3467

International Standard Serial Number (ISSN)

  • 1540-3459

Digital Object Identifier (DOI)

  • 10.1137/18M1166432

Citation Source

  • Scopus