SC16 Salt Lake City, UT

86. STRUMPACK: Scalable Preconditioning Using Low-Rank Approximations and Random Sampling


Authors: Pieter Ghysels (Lawrence Berkeley National Laboratory)Xiaoye S. Li (Lawrence Berkeley National Laboratory)Christopher Gorman (University of California, Santa Barbara)Francois-Henry Rouet (Lawrence Berkeley National Laboratory)

Abstract: We present a parallel and fully algebraic preconditioner based on an approximate sparse factorization using rank-structured matrix compression. In sparse multifrontal LU factorization, the fill-in occurs in dense frontal matrices. These are approximated as Hierarchically Semi-Separable (HSS) rank-structured matrices using an efficient randomized sampling technique. The resulting fast solver or preconditioner has optimal or close to optimal complexity – in terms of floating point operations and memory usage – for matrices from several types of discretized partial differential equations. Our STRUMPACK approximate solver is a viable alternative to other state-of-the-art preconditioners like ILU and AMG, and we demonstrate that our new method is more robust and scalable than existing ones. Our poster presents results with the distributed memory MPI+OpenMP code for DOE applications on supercomputers from NERSC.

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