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

2018/09/12 by Julien Molina, Molina, Julien, Richard Mikaël Slevinsky +1 · 1 citation
Computer Science · Engineering · Mathematics · #33C55 #65F35 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Computer Graphics and Visualization Techniques #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1809.04555

openalex publication_date 2018/09/12 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

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.

Cited by

• Nonlocal vector calculus on the sphere

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