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arXiv · 1809.04555

A rapid and well-conditioned algorithm for the Helmholtz--Hodge decomposition of vector fields on the sphere

Julien Molina·Richard Mikael Slevinsky
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Abstract

A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as barely-overdetermined banded linear systems, and solves them with banded $QR$ decompositions that factor and execute in optimal complexity. Rigorous upper bounds on the $2$-norm relative condition number of the banded linear systems support the observable low error growth with respect to truncation degree.

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Julien Molina, Richard Mikael Slevinsky. 2018-09-12. A rapid and well-conditioned algorithm for the Helmholtz--Hodge decomposition of vector fields on the sphere. https://arxiv.org/abs/1809.04555

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