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Accuracy and speed in computing the Chebyshev collocation derivativeWe studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.
Document ID
19920003815
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Don, Wai-Sun (Brown Univ. Providence, RI, United States)
Solomonoff, Alex (Brown Univ. Providence, RI, United States)
Date Acquired
September 6, 2013
Publication Date
December 1, 1991
Publication Information
Publisher: NASA
Subject Category
Aerodynamics
Report/Patent Number
NAS 1.26:4411
NASA-CR-4411
Accession Number
92N13033
Funding Number(s)
PROJECT: RTOP 505-62-40-07
CONTRACT_GRANT: NAG1-1145
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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