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arXiv · 1712.07297

A distributed-memory hierarchical solver for general sparse linear systems

Chao Chen·Hadi Pouransari·Sivasankaran Rajamanickam·Erik G. Boman·Eric Darve
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Abstract

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.

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Chao Chen, Hadi Pouransari, Sivasankaran Rajamanickam, Erik G. Boman, Eric Darve. 2017-12-20. A distributed-memory hierarchical solver for general sparse linear systems. https://arxiv.org/abs/1712.07297

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