Comparison of several approximation schemes on the Cubed Sphere
- 1Université de Lorraine, Institue Elie Cartan de Lorraine, Mathématiques, Metz, France (jean-pierre.croisille@univ-lorraine.fr)
- 2Université de Lorraine, CNRS, IECL, F-57000 Metz, France
- 3Laboratoire de Mathématiques et Applications, Université de Poitiers, CNRS, F-86073 Poitiers, France
Approximation, interpolation and quadrature are questions of fundamental
importance for atmospheric and oceanic problems at planetary scale.
Computation with spherical harmonics on the sphere is an old mathematical topic; it has a particular interest in geosciences, and is still an active field of research. In this poster, we will show numerical comparisons of several approximation schemes, with a special focus on the Cubed Sphere grid. We test hyperinterpolation, weighted least squares, and interpolation on a series of test functions with various smoothness properties. Our last results include the derivation of explicit formulas for optimal quadrature rules on low resolution Cubed Spheres.
[1] J.-B. Bellet, M. Brachet, and J.-P. Croisille, Interpolation on the Cubed Sphere with Spherical Harmonics, Numerische Mathematik, 153 (2023), pp. 249-278.
[2] J.-B. Bellet and J.-P. Croisille, Least Squares Spherical Harmonics Approximation on the Cubed Sphere, Journal of Computational and Applied Mathematics, 429 (2023), 115213.
[3] C. An and H.-N. Wu, Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere, Journal of Complexity, 80 (2024), 101789.
How to cite: Croisille, J.-P., Bellet, J.-B., and Brachet, M.: Comparison of several approximation schemes on the Cubed Sphere, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-15777, https://doi.org/10.5194/egusphere-egu24-15777, 2024.
