A task-based distributed parallel sparsified nested dissection algorithm

Abstract

Sparsified nested dissection (spaND) is a fast scalable linear solver for sparse linear systems. It combines nested dissection and separator sparsification, leading to an algorithm with an O(N log N ) complexity on many problems. In this work, we study the parallelization of spaND using TaskTorrent, a lightweight, distributed, task-based runtime in C++. This leads to a distributed version of spaND using a task-based runtime system. We explain how to adapt spaND's partitioning for parallel execution, how to increase concurrency using a simultaneous sparsification algorithm, and how to express the DAG using TaskTorrent. We then benchmark spaND on a few large problems. spaND exhibits good strong and weak scalings, efficiently using up to 9,000 cores when ranks grow slowly with the problem size. CCS CONCEPTS• Mathematics of computing → Computations on matrices; • Computing methodologies → Parallel programming languages.