parGeMSLR: A Parallel Multilevel Schur Complement Low-Rank Preconditioning and Solution Package for General Sparse Matrices

TL;DR

parGeMSLR is a parallel C++/MPI library that efficiently solves large sparse linear systems using a multilevel Schur complement low-rank preconditioner, optimized for distributed-memory and hybrid GPU environments.

Contribution

It introduces a novel multilevel Schur complement low-rank preconditioning approach integrated into a scalable software library for sparse linear systems.

Findings

Demonstrates good weak and strong scaling on 3D PDE discretizations.

Effectively leverages hybrid CPU-GPU architectures.

Provides a flexible, parallel solution for large sparse systems.

Abstract

This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner implemented in parGeMSLR is based on algebraic domain decomposition and partitions the symmetrized adjacency graph recursively into several non-overlapping partitions via a p-way vertex separator, where p is an integer multiple of the total number of MPI processes. From a numerical perspective, parGeMSLR builds a Schur complement approximate inverse preconditioner as the sum between the matrix inverse of the interface coupling matrix and a low-rank correction term. To reduce the cost associated with the computation of the approximate inverse matrices, parGeMSLR exploits a multilevel partitioning of the algebraic domain. The parGeMSLR library is implemented on top of the Message Passing Interface and can solve both real and complex linear systems. Furthermore, parGeMSLR can take advantage of hybrid computing environments with in-node access to one or more Graphics Processing Units. Finally, the parallel efficiency (weak and strong scaling) of parGeMSLR is demonstrated on a few model problems arising from discretizations of 3D Partial Differential Equations.