Parallel Sparse and Data-Sparse Factorization-based Linear Solvers

TL;DR

This paper reviews recent advances in parallel sparse direct solvers, focusing on reducing communication costs and computational complexity through low-rank and hierarchical matrix techniques, to improve scalability and efficiency on modern parallel hardware.

Contribution

It provides a comprehensive overview of recent algorithmic developments and parallelization strategies for sparse direct solvers, emphasizing communication reduction and low-rank compression methods.

Findings

Enhanced parallelization strategies for sparse solvers.

Reduction in communication and latency costs.

Improved computational efficiency using low-rank techniques.

Abstract

Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their robustness and accuracy, direct solvers are crucial components in building a scalable solver toolchain. In this article, we will review recent advances of sparse direct solvers along two axes: 1) reducing communication and latency costs in both task- and data-parallel settings, and 2) reducing computational complexity via low-rank and other compression techniques such as hierarchical matrix algebra. In addition to algorithmic principles, we also illustrate the key parallelization challenges and best practices to deliver high speed and reliability on modern heterogeneous parallel machines.