Nonuniform sampling and multiscale computation

Björn Engquist, Christina Frederick

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In homogenization theory and multiscale modeling, typical functions satisfy the scaling law fε(x) = f(x, x/ε), where f is periodic in the second variable and ε is the smallest relevant wavelength, 0 < ε 1. Our main result is a new L2-stability estimate for the reconstruction of bandlimited multiscale functions fε from periodic nonuniform samples. The goal of this paper is to demonstrate the close relation between sampling strategies developed in information theory and computational grids in multiscale modeling. This connection is of much interest because numerical simulations often involve discretizations by means of sampling, and the proposed sampling sets are of optimal rate according to the minimal sampling requirements of Landau [Proc. IEEE, 55 (1967), pp. 1701-1706].

Original languageEnglish (US)
Pages (from-to)1890-1901
Number of pages12
JournalMultiscale Modeling and Simulation
Volume12
Issue number4
DOIs
StatePublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

Keywords

  • Heterogeneous multiscale method
  • Multiscale functions
  • Nonuniform periodic sampling
  • Shannon's sampling theorem

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