We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We present various numerical results to demonstrate the versatility and scalability of the parallel algorithm.
@article{arxiv.1712.07297,
title = {A distributed-memory hierarchical solver for general sparse linear systems},
author = {Chao Chen and Hadi Pouransari and Sivasankaran Rajamanickam and Erik G. Boman and Eric Darve},
journal= {arXiv preprint arXiv:1712.07297},
year = {2017}
}