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arXiv · 1608.04436

Pseudo-spectral methods for the Laplace-Beltrami equation and the Hodge decomposition on surfaces of genus one

Lise-Marie Imbert-Gerard·Leslie Greengard
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Abstract

The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning to com- putational physics. Here, we present a high-order accurate pseudo-spectral approach, applicable to closed surfaces of genus one in three dimensional space, with a view toward applications in plasma physics and fluid dynamics.

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Lise-Marie Imbert-Gerard, Leslie Greengard. 2016-08-15. Pseudo-spectral methods for the Laplace-Beltrami equation and the Hodge decomposition on surfaces of genus one. https://doi.org/10.1002/num.22131

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