Quadrature and symmetry on the Cubed Sphere

Jean-Baptiste Bellet (1) , Matthieu Brachet (2) , Jean-Pierre Croisille (1)

1 IECL - Institut Élie Cartan de Lorraine
2 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

In the companion paper [J.-B. Bellet, M. Brachet & J.-P. Croisille, Interpolation on the Cubed Sphere with Spherical Harmonics, Preprint, 2021], a spherical harmonics subspace associated to the Cubed Sphere has been introduced. This subspace is further analyzed here. In particular, it permits to dene a new Cubed Sphere based quadrature. This quadrature inherits the rotationally invariant properties of the spherical harmonics subspace. Contrary to Gauss quadratures, where the set of nodes and weights is solution of a nonlinear system, only the weights are unknown here. Despite this conceptual simplicity, the new quadrature displays an accuracy comparable to optimal quadratures, such as the Lebedev rules.

Mots clés: Cubed sphere; interpolation; quadrature; octahedral group

Domaines: Analyse numérique [math.NA]

Jean-Baptiste Bellet, Matthieu Brachet, Jean-Pierre Croisille. Quadrature and symmetry on the Cubed Sphere. 2021. ⟨hal-03223150⟩