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# Reordering CAE Matrix using Hierarchical Clustering

*Proceedings of 2024 International Conference on Machine Learning and Intelligent Computing*, PMLR 245:413-420, 2024.

#### Abstract

Traversing a high-dimensional mesh using 1-D trajectory is a widely used technique in the ﬁelds of CAE computing and data management. Such a trajectory is widely known as a space-ﬁlling curve. Nevertheless, most of the space ﬁlling curves, such as Z-curve or Hilbert curve, are designed for structured meshes. Therefore, it is vital to design an effective space-ﬁlling curve for unstructured meshes. In this paper, we propose a space-ﬁlling curve for unstructured mesh by considering the original problem as a graph clustering problem. We generate a hierarchical clustering schema and uses depth-ﬁrst search to traverse the hierarchical schema. In this way, the sequence of the depth-ﬁrst search naturally be-comes a 1-D trajectory. Compared with traditional space-ﬁlling curves, our solution can effectively handle traversing problems on unstructured meshes.