Title: Efficient Spectral-Galerkin Methods IV. Spherical geometries

Author: Jie Shen

Status: Submitted to SIAM J. Sci. Comput.

Abstract:

Fast spectral-Galerkin algorithms are developed 
for elliptic equations on the sphere. The algorithms are
based on a double Fourier expansion and 
have quasi-optimal (optimal up to a logarithmic term) computational
complexity. Numerical experiments indicate that they are significantly
more
efficient and/or accurate when compared with the algorithms based
on spherical harmonics and on finite difference. 
Extensions to problems in spherical layers and to
vector equations are also discussed.