Distributed Topological Data Analysis of Tetrahedral Meshes With Apache Spark

Tetrahedral meshes are essential for scientific computing due to their flexibility in capturing complex geometries, yet their irregular structure imposes significant memory and performance challenges when applied at scale. Distributed processing can alleviate these limitations, but traditional MPI-based solutions often require substantial redesign of algorithms to manage communication and data distribution. In this work, we introduce Tetra-Spark, a framework for distributed representation and analysis of large tetrahedral meshes built on Apache Spark. Leveraging Spark's implicit data parallelism and in-memory execution model, Tetra-Spark enables scalable mesh encoding, connectivity computation, and topological analysis without the need for low-level distributed programming. To prove the effectiveness and scalability of such a framework, we conduct a comprehensive comparison against a vanilla Spark implementation and an MPI-supported implementation. Our experimental evaluation shows that Tetra-Spark achieves up to a 78× speedup and reduces memory usage by up to 80% when retrieving connectivity relations. This optimized design further accelerates subsequent morphology computations, resulting in up to a 55.6× speedup for computing local topological features, and from 15.2× to 173.6× for extracting global topological descriptors.