Basker: A Threaded Sparse LU Factorization Utilizing Hierarchical Parallelism and Data Layouts

TL;DR

Basker is a scalable sparse LU factorization solver that leverages hierarchical parallelism and data layouts to improve performance on modern architectures, outperforming existing solvers significantly.

Contribution

It introduces a new parallel algorithm for sparse LU factorization that aligns with hierarchical hardware architectures and memory layouts.

Findings

Achieves up to 7.4x speedup on Xeon Phi compared to KLU.

Outperforms Intel MKL Pardiso by up to 53x on CPU.

Provides 5.4x speedup on challenging circuit matrices.

Abstract

Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to parallelize the Gilbert-Peierls algorithm for sparse LU factorization. As architectures evolve, there exists a need for algorithms that are hierarchical in nature to match the hierarchy in thread teams, individual threads, and vector level parallelism. Basker is designed to map well to this hierarchy in architectures. There is also a need for data layouts to match multiple levels of hierarchy in memory. Basker uses a two-dimensional hierarchical structure of sparse matrices that maps to the hierarchy in the memory architectures and to the hierarchy in parallelism. We present performance evaluations of Basker on the Intel SandyBridge and Xeon Phi platforms using circuit and power grid matrices taken from the University of Florida sparse matrix collection and from Xyce circuit simulations. Basker achieves a geometric mean speedup of 5.91x on CPU (16 cores) and 7.4x on Xeon Phi (32 cores) relative to KLU. Basker outperforms Intel MKL Pardiso (PMKL) by as much as 53x on CPU (16 cores) and 13.3x on Xeon Phi (32 cores) for low fill-in circuit matrices. Furthermore, Basker provides 5.4x speedup on a challenging matrix sequence taken from an actual Xyce simulation.