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Spectral Reconstruction of Piecewise Smooth Functions from Their Discrete Data

Published online by Cambridge University Press:  15 May 2002

Anne Gelb  and
Eitan Tadmor
Anne Gelb
Affiliation:
Department of Mathematics, P.O. Box 871804, Arizona State University, Tempe, AZ 85287-1804, USA. [email protected].
Eitan Tadmor
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA. [email protected].
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Abstract

This paper addresses the recovery of piecewise smooth functions from their discrete data.Reconstruction methods using both pseudo-spectral coefficients andphysical space interpolants have been discussed extensively in theliterature, and it is clear that an a priori knowledge of the jumpdiscontinuity location is essential for any reconstruction techniqueto yield spectrally accurate results with high resolution near thediscontinuities. Hence detection of the jump discontinuities iscritical for all methods. Here we formulate a new localized reconstruction method adapted from themethod 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 methodis robust and highly accurate, yielding spectral accuracy up to a smallneighborhood of the jump discontinuities. Results are shown inone and two dimensions.

Keywords

Edge detectionnonlinear enhancementconcentration methodpiecewise smoothnesslocalized reconstruction.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 2 , March 2002 , pp. 155 - 175
Copyright
© EDP Sciences, SMAI, 2002

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