Abstract A number of methods for studying the large-scale cosmic matter distribution exist in the literature. One particularly common method employed to define the cosmic web is to examine the density, velocity or potential field. Such methods are advantageous since a Hessian matrix can be constructed whose eigenvectors (and eigenvalues) indicate the principal directions (and strength) of local collapse or expansion. Technically this is achieved by diagonalizing the Hessian matrix using a fixed finite grid. The resultant large-scale structure quantification is thus inherently limited by the grid’s finite resolution. Here, we overcome the obstacle of finite grid resolution by introducing a new method to determine halo environment using an adaptive interpolation which is more robust to resolution than the typical “Nearest Grid Point” (NGP) method. Essentially instead of computing and diagonalizing the Hessian matrix once for the entire grid, we suggest doing so once for each halo or galaxy in question. We examine how the eigenvalues and eigenvector direction’s computed using our algorithm and the NGP method converge for different grid resolutions, finding that our new method is convergent faster. Namely changes of resolution have a much smaller effect than in the NGP method. We therefore suggest this method for future use by the community.

中文翻译：

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宇宙场中晕环境的稳健确定

摘要 文献中有多种研究大尺度宇宙物质分布的方法。定义宇宙网的一种特别常用的方法是检查密度、速度或势场。此类方法是有利的，因为可以构建 Hessian 矩阵，其特征向量（和特征值）指示局部坍塌或膨胀的主要方向（和强度）。从技术上讲，这是通过使用固定的有限网格对角化 Hessian 矩阵来实现的。因此，由此产生的大规模结构量化本质上受到网格有限分辨率的限制。在这里，我们通过引入一种使用自适应插值确定光晕环境的新方法来克服有限网格分辨率的障碍，该方法比典型的“最近网格点”（NGP）方法对分辨率更鲁棒。本质上，不是为整个网格计算和对角化 Hessian 矩阵一次，我们建议对每个有问题的光晕或星系进行一次。我们检查了使用我们的算法和 NGP 方法计算的特征值和特征向量方向如何针对不同的网格分辨率收敛，发现我们的新方法收敛速度更快。即分辨率的变化比 NGP 方法的影响要小得多。因此，我们建议社区将来使用这种方法。即分辨率的变化比 NGP 方法的影响要小得多。因此，我们建议社区将来使用这种方法。即分辨率的变化比 NGP 方法的影响要小得多。因此，我们建议社区将来使用这种方法。