论文标题
杂技：在球形三角形上证明是准确稳定的数值集成
ARPIST: Provably Accurate and Stable Numerical Integration over Spherical Triangles
论文作者
论文摘要
在球体上的数值集成，包括球形三角形区域的计算，是地貌的核心计算。常用技术有时会遭受不稳定性和明显的准确性丧失。我们描述了一种称为arpist的新算法，用于在球形三角形上的函数的准确整合。 Arpist是基于易于实现的转换，从其相应的线性三角形通过径向投影，以实现高精度和效率。更重要的是，Arpist克服了计算转化的雅各布式的潜在不稳定性，即使是由于避免潜在的灾难性圆形误差，即使形状差的三角形也可能发生在极度经度的纬度网格中。我们将提出的技术与L'Huilier的计算计算球形三角形区域进行了比较，还将其与最近开发的LSQST方法进行了比较（J. Beckmann，H.N。Mhaskar和J. Prestin，Gem-Int。J.Geomath。 Appl。Math。，137：174-188，2015）用于在球形三角形上的平滑功能。我们的结果表明，Arpist可以比以前的方法具有卓越的准确性和稳定性，同时更快，更容易实施数量级。
Numerical integration on spheres, including the computation of the areas of spherical triangles, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We describe a new algorithm, called ARPIST, for accurate and stable integration of functions on spherical triangles. ARPIST is based on an easy-to-implement transformation to the spherical triangle from its corresponding linear triangle via radial projection to achieve high accuracy and efficiency. More importantly, ARPIST overcomes potential instabilities in computing the Jacobian of the transformation, even for poorly shaped triangles that may occur at poles in regular longitude-latitude meshes, by avoiding potential catastrophic rounding errors. We compare our proposed technique with L'Huilier's Theorem for computing the area of spherical triangles, and also compare it with the recently developed LSQST method (J. Beckmann, H.N. Mhaskar, and J. Prestin, GEM - Int. J. Geomath., 5:143-162, 2014) and a radial-basis-function-based technique (J. A. Reeger and B. Fornberg, Stud. Appl. Math., 137:174-188, 2015) for integration of smooth functions on spherical triangulations. Our results show that ARPIST enables superior accuracy and stability over previous methods while being orders of magnitude faster and significantly easier to implement.
