parRSB: Exascale Spectral Element Mesh Partitioning
2026-06-12 • Distributed, Parallel, and Cluster Computing
Distributed, Parallel, and Cluster Computing
AI summaryⓘ
The authors developed parRSB, a tool that splits very large mesh graphs into smaller parts efficiently and in parallel, which helps in managing complex calculations. Their method uses a mathematical concept called the Fiedler vector to decide where to cut the graph to reduce communication between parts. They tested two ways to find this vector and showed that parRSB works well on some of the fastest supercomputers. The authors also improved their method to make it faster.
graph partitioningspectral element meshRecursive Spectral BisectionFiedler vectorLaplacian matrixLanczos methodInverse iterationConjugate Gradient methodparallel computingsupercomputers
Authors
Thilina Ratnayaka, Paul Fischer
Abstract
We introduce parRSB - a parallel, highly scalable graph partitioner for spectral element meshes that produce high quality partitions. parRSB is based on Recursive Spectral Bisection (RSB) algorithm implemented on the dual graph of the input mesh. RSB uses the Fiedler vector, which is the eigenvector associated with the smallest non-zero eigenvalue of the Laplacian matrix of the dual graph for making partitioning decisions and tries to minimize the communication volume between the partitions. We implemented two numerical methods: Lanczos, and Inverse iteration using Conjugate Gradient method to compute the Fiedler vector. We present partitioning results using parRSB on Summit and Frontier supercomputers at Oak Ridge National Laboratory to illustrate the quality of the partitions produced by parRSB and the scalability of our implementation. We also present results for some of the optimizations we did to speed up the partitioning process.