Welcome to ARPIST Project

Introduction

Welcome to the ARPIST package! ARPIST stands for Anchored Radially Projected with Integration on Spherical Triangles, which is a quadrature rule generator for accurate and stable integration of functions on spherical triangles. ARPIST is based on an efficient and easy-to-implement transformation to the spherical triangle from its corresponding linear triangle via radial projection to achieve high accuracy and efficiency.

Installation

To download the latest version of the code, use the command

git clone https://github.com/numgeom/ARPIST.git

Use git pull to download any new changes added since git clone or last git pull. Alternatively, use git checkout v[GLOBAL].[MAJOR].[MINOR] to download a specific version.

Usage

We provide the matlab and python implementation and three coarse test meshes for the demo scripts.

For the matlab implementation, please see the test_integration_over_whole_sphere.m for example. We use compute_sphere_quadrature to generate quadrature points and corresponding weights on the sphere, which could be reused for the integration of different functions. We also provide another implementation spherical_integration for integration over some spherical polygons.

For the python implementation, please see the test_integration_over_whole_sphere.py and test_one_eighth_area.py for example. Please import compute_sphere_quadrature as a module that provides two public interfaces. One is compute_sphere_quadrature for the generation of quadrature points and corresponding weights on the sphere, which could be reused for integration of different functions. The other is spherical_integration for integration over some spherical polygons. We provide the quadrature rule table for the reference triangle on a 2D plane in quadrature_rule.py, which can be rewritten to set up your favorite quadrature rule.

Copyright and Licenses

BSD 3-Clause License

Copyright (c) 2022, NumGeom Group at Stony Brook University All rights reserved.

How to Cite ARPIST

If you use ARPIST in your research for nonsingular systems, please cite the ARPIST paper:

@article{li2022arpist,
  title={ARPIST: Provably Accurate and Stable Numerical Integration over Spherical Triangles},
  author={Li, Yipeng and Jiao, Xiangmin},
  journal={arXiv preprint arXiv:2201.00261},
  year={2022}
}

Contacts

• Yipeng Li, yipeng.li@stonybrook.edu, jamesonli1313@gmail.com
• Xiangmin Jiao, xiangmin.jiao@stonybrook.edu, xmjiao@gmail.com