surfgeopy

Calculating approximations of surface integrals over smooth embedded manifolds

This Python package rests on curved surface triangulations realised due to 𝑘th-order interpolation of the closest point projection, extending initial linear surface approximations. It achieves this by employing a novel technique called square-squeezing, which involves transforming the interpolation tasks of triangulated manifolds to the standard hypercube using a cube-to-simplex transformation that has been recently introduced. To ensure the stability and accuracy of the computations, surfgeopy leverages classic Chebyshev-Lobatto grids. These grids enable the calculation of high-order interpolants for the surface geometry while avoiding Runge’s phenomenon, a common issue in numerical analysis.

surfgeopy is freely available and open-source. Its purpose is to calculate approximations of surface integrals over smooth embedded manifolds. The package is based on a publication presenting a novel methodology for deriving high-order quadrature rules designed for the integration of scalar functions over regular embedded manifolds.

Further information:

https://github.com/casus/surfgeopy

Reference:

Zavalani, G.; Sander, O.; Hecht, M. (2023). High-Order Integration on regular triangulated manifolds reaches Super-Algebraic Approximation Rates through Cubical Re-parameterizations. arxiv.org. https://arxiv.org/abs/2311.13909

Download:

https://zenodo.org/records/12704560

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