Interpolation on the cubed sphere with spherical harmonics. (English) Zbl 1531.65022
Summary: We consider Lagrange interpolation with Spherical Harmonics of data located at the equiangular Cubed Sphere nodes. An approach based on a suitable Echelon Form of the associated Vandermonde matrix is carried out. As an outcome, a particular subspace of Spherical Harmonics is defined. This subspace possesses a high-frequency truncation, reminiscent of the rhomboidal truncation. Numerical results show the interest of this approach in various contexts. In particular, several examples of resolution of the Poisson equation on the sphere are displayed.
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