TY - JOUR
T1 - Mappings and accuracy for Chebyshev pseudo-spectral approximations
AU - Bayliss, Alvin
AU - Turkel, Eli
N1 - Funding Information:
* This research was partially supported Space Administration while the authors NASA Lewis Research Center, Cleveland, was also provided by NSF Grants ASC
PY - 1992/8
Y1 - 1992/8
N2 - The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in applications. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than the original function. The effect on the approximation of introducing subdomains is also studied. The accuracy of the pseudo-spectral approximation is very sensitive to the location of the interface, although this sensitivity is reduced when mappings are employed within the subdomains.
AB - The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in applications. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than the original function. The effect on the approximation of introducing subdomains is also studied. The accuracy of the pseudo-spectral approximation is very sensitive to the location of the interface, although this sensitivity is reduced when mappings are employed within the subdomains.
UR - http://www.scopus.com/inward/record.url?scp=28144442068&partnerID=8YFLogxK
U2 - 10.1016/0021-9991(92)90012-N
DO - 10.1016/0021-9991(92)90012-N
M3 - מאמר
AN - SCOPUS:28144442068
VL - 101
SP - 349
EP - 359
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
IS - 2
ER -