High-order covariant differentiation in applications to Helmholtz-Hodge decomposition on curved surfaces

Sehun Chun

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arXiv · 2004.14153

High-order covariant differentiation in applications to Helmholtz-Hodge decomposition on curved surfaces

Sehun Chun

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Abstract

A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which would deteriorate the accuracy of the covariant derivative and prevent its application to complex surfaces. As an application, the Helmholtz-Hodge decomposition (HHD) is adapted in the context of the Galerkin method for displaying the irrotational, incompressible, and harmonic components of vectors on curved surfaces.

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Sehun Chun. 2020-04-27. High-order covariant differentiation in applications to Helmholtz-Hodge decomposition on curved surfaces. https://arxiv.org/abs/2004.14153

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