Interpolation on the cubed sphere with spherical harmonics

Abstract

We consider the Lagrange interpolation with Spherical Harmonics of data located on the equiangular Cubed Sphere. A new 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 dened. 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.

Least squares spherical harmonics approximation on the Cubed Sphere

“…In [4], we have introduced a particular SH subspace with good interpolating properties on the Cubed Sphere (Lagrange interpolation). This space consists of the direct sum…”