Title: A distributed-memory hierarchical solver for general sparse linear systems,
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.