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Advances in Computational Mathematics

, Volume 40, Issue 5–6, pp 1169–1184 | Cite as

On spherical harmonics based numerical quadrature over the surface of a sphere

  • Bengt FornbergEmail author
  • Jordan M. Martel
Article

Abstract

It has been suggested in the literature that different quasi-uniform node sets on a sphere lead to quadrature formulas of highly variable quality. We analyze here the nature of these variations, and describe an easy-to-implement least-squares remedy for previously problematic cases. Quadrature accuracies are then compared for different node sets ranging from fully random to those based on Gaussian quadrature concepts.

Keywords

Quadrature Sphere Spherical harmonics ME nodes MD nodes Gaussian quadrature 

Mathematics Subject Classifications (2010)

65D30 65D32 41A55 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of Colorado at BoulderBoulderUSA
  2. 2.Leeds School of BusinessUniversity of Colorado at BoulderBoulderUSA

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