Spectral reconstruction of piecewise smooth functions from their discrete data

Anne Gelb, Eitan Tadmor

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurate results with high resolution near the discontinuities. Hence detection of the jump discontinuities is critical for all methods. Here we formulate a new localized reconstruction method adapted from the method developed in Gottlieb and Tadmor (1985) and recently revisited in Tadmor and Tanner (in press). Our procedure incorporates the detection of edges into the reconstruction technique. The method is robust and highly accurate, yielding spectral accuracy up to a small neighborhood of the jump discontinuities. Results are shown in one and two dimensions.

Original languageEnglish (US)
Pages (from-to)155-175
Number of pages21
JournalMathematical Modelling and Numerical Analysis
Volume36
Issue number2
DOIs
StatePublished - 2002

Keywords

  • Concentration method
  • Edge detection
  • Localized reconstruction
  • Nonlinear enhancement
  • Piecewise smoothness

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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