parRSB: Exascale Spectral Element Mesh Partitioning

2026-06-12

AI Summary

This work proposes a highly scalable parallel recursive spectral bisection (parRSB) method tailored for Exascale computing to address the challenge of efficient, high-quality graph partitioning of large-scale spectral element meshes. The approach computes the Fiedler vector in parallel on the mesh dual graph by integrating the Lanczos algorithm with conjugate gradient-based inverse iteration, augmented with several numerical optimization strategies to enhance computational efficiency. Experimental results on the Summit and Frontier supercomputing platforms demonstrate that parRSB significantly reduces communication overhead while preserving partition quality, exhibiting excellent strong and weak scalability as well as superior partitioning speedup.

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.

Problem

• spectral element mesh
• graph partitioning
• exascale
• parallel partitioning
• communication volume

Innovation

• Recursive Spectral Bisection
• Fiedler vector
• spectral element mesh partitioning
• parallel graph partitioning
• exascale computing