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Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity
Mulholland, L. S. Huang, Weizhang Sloan, David M.
Mulholland, L. S.
Huang, Weizhang
Sloan, David M.
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Abstract
The work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions. The approach makes use of the adaptive finite difference method presented by Huang and Sloan [SIAM J. Sci. Comput., 15 (1994), pp. 776--797]. This method is applied on a coarse grid to obtain a rough approximation of the solution and a suitable adapted mesh. The adaptive finite difference solution permits the construction of a smooth coordinate transformation that relates the computational space to the physical space. The map between the spaces is based on Chebyshev polynomial interpolation. Finally, the standard pseudospectral (PS) method is applied to the transformed differential problem to obtain highly accurate, nonoscillatory numerical solutions. Numerical results are presented for steady problems in one and two space dimensions.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/S1064827595291984.
Date
1998-07-01
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Publisher
Society for Industrial and Applied Mathematics
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Keywords
adaptivity, equidistribution, pseudospectral, differential, equations
Citation
Mulholland, L. S., Huang, Weizhang., Sloan, D. M. "Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity." SIAM J. Sci. Comput., 19(4), 1261–1289. (29 pages). http://dx.doi.org/10.1137/S1064827595291984.