Efficient Spectral-Galerkin Methods IV. Spherical Geometries

Authors:
Jie Shen
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1999

Citing 0
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Navier-Stokes spectral solver in a sphere

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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.