We present a parallel hierarchical solver for general sparse linear systemson distributed-memory machines. For large-scale problems, this fully algebraicalgorithm is faster and more memory-efficient than sparse direct solversbecause it exploits the low-rank structure of fill-in blocks. Depending on theaccuracy of low-rank approximations, the hierarchical solver can be used eitheras a direct solver or as a preconditioner. The parallel algorithm is based ondata decomposition and requires only local communication for updating boundarydata on every processor. Moreover, the computation-to-communication ratio ofthe parallel algorithm is approximately the volume-to-surface-area ratio of thesubdomain owned by every processor. We present various numerical results todemonstrate the versatility and scalability of the parallel algorithm.
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