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Fast Spherical/Harmonic Spline Modeling

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Handbook of Geomathematics

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.

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Authors and Affiliations

  1. Geomathematics Group, University of Siegen, Siegen, Germany

    Martin Gutting

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  1. Martin Gutting
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Correspondence to Martin Gutting .

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Editors and Affiliations

  1. Geomathematische Gruppe, TU Kaiserslautern FB Mathematik, Kaiserslautern, Germany

    Willi Freeden

  2. University of Central Florida Dept. Mathematics, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Inst. Analysis, TU Braunschweig FB 1 Mathematik und Informatik, Braunschweig, Germany

    Thomas Sonar

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Gutting, M. (2013). Fast Spherical/Harmonic Spline Modeling. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27793-1_47-1

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  • DOI: https://doi.org/10.1007/978-3-642-27793-1_47-1

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  • Online ISBN: 978-3-642-27793-1

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