Efficient representation and analysis for a large tetrahedral mesh using Apache Spark

Yuehui Qian, Guoxi Liu, Federico Iuricich, Leila De Floriani

Abstract: Tetrahedral meshes are widely used due to their flexibility and adaptability in representing changes of complex geometries and topology. However, most existing data structures struggle to efficiently encode the irregular connectivity of tetrahedral meshes with billions of vertices. We address this problem by proposing a novel framework for efficient and scalable analysis of large tetrahedral meshes using Apache Spark. The proposed framework, called Tetra-Spark, features optimized approaches to locally compute many connectivity relations by first retrieving the Vertex-Tetrahedron (VT) relation. This strategy significantly improves Tetra-Spark’s efficiency in performing morphology computations on large tetrahedral meshes. To prove the effectiveness and scalability of such a framework, we conduct a comprehensive comparison against a vanilla Spark implementation for the analysis of tetrahedral meshes. Our experimental evaluation shows that Tetra-Spark achieves up to a $78 \times$ speedup and reduces memory usage by up to 80% when retrieving connectivity relations with the VT relation available. This optimized design further accelerates subsequent morphology computations, resulting in up to a $47.7 \times$ speedup.