The Morse-Smale complex is a well studied topological structure that represents the gradient flow behavior of a scalar function. It supports multi-scale topological analysis and visualization of large scientific data. Its computation poses significant algorithmic challenges when considering large scale data and increased feature complexity. Several parallel algorithms have been proposed towards the fast computation of the 3D Morse-Smale complex. The non-trivial structure of the saddle-saddle connections are not amenable to parallel computation. This paper describes a fine grained parallel method for computing the Morse-Smale complex that is implemented on a GPU. The saddle-saddle reachability is first determined via a transformation into a sequence of vector operations followed by the path traversal, which is achieved via a sequence of matrix operations. Computational experiments show that the method achieves up to 7x speedup over current shared memory implementations.

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Morse-Smale 复数的 GPU 并行计算

Morse-Smale 复合体是一种经过充分研究的拓扑结构，它表示标量函数的梯度流动行为。支持大科学数据的多尺度拓扑分析和可视化。在考虑大规模数据和增加的特征复杂性时，它的计算提出了重大的算法挑战。已经提出了几种并行算法来快速计算 3D Morse-Smale 复合体。鞍鞍连接的非平凡结构不适合并行计算。本文描述了一种用于计算在 GPU 上实现的 Morse-Smale 复数的细粒度并行方法。鞍鞍可达性首先通过转换为一系列向量操作然后进行路径遍历来确定，这是通过一系列矩阵运算来实现的。计算实验表明，与当前的共享内存实现相比，该方法实现了高达 7 倍的加速。