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    Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity

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    HuangW_SJoNA_19(4)1261.pdf (787.5Kb)
    Issue Date
    1998-07-01
    Author
    Mulholland, L. S.
    Huang, Weizhang
    Sloan, David M.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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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.
    URI
    http://hdl.handle.net/1808/16879
    DOI
    https://doi.org/10.1137/S1064827595291984
    Collections
    • Mathematics Scholarly Works [273]
    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.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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