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Fast Spherical/Harmonic Spline Modeling

In: Handbook of Geomathematics

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  • Martin Gutting

    (University of Siegen, Geomathematics Group)

Abstract

Spherical and harmonic splines are closely related approaches to solve interpolation/approximation as well as boundary value problems on the sphere and on regular (sphere-like) surfaces, respectively. In any case they lead to a system of linear equations which requires fast summation methods for the kernel sums. The fast multipole method achieves just that and is combined in this paper with a preconditioner using the same decomposition of the computational domain to solve the system of linear equations resulting from spherical/harmonic splines. Due to the localizing nature of splines, regional problems can also be treated with this approach.

Suggested Citation

  • Martin Gutting, 2015. "Fast Spherical/Harmonic Spline Modeling," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 2711-2746, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_47
    DOI: 10.1007/978-3-642-54551-1_47
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