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DTSTAMP:20210402T160558Z
LOCATION:Poster Module
DTSTART;TZID=America/New_York:20201118T083000
DTEND;TZID=America/New_York:20201118T170000
UID:submissions.supercomputing.org_SC20_sess340_spostu118@linklings.com
SUMMARY:Randomized Cholesky Factorization in Parallel
DESCRIPTION:ACM Student Research Competition: Graduate Poster, ACM Student
Research Competition: Undergraduate Poster, Posters\n\nRandomized Cholesk
y Factorization in Parallel\n\nLiang\n\nLarge sparse SDD (symmetric diagon
ally dominant) linear systems arise from solving elliptic PDEs and graph p
roblems. Exact Cholesky factorization leads to excessive fill-in, especial
ly in 3D. Our approach is to subsample the (dense) Schur complement update
and construct an (approximate) sparse preconditioner. To optimize for pra
ctical performance, we reorder the original matrix to exploit the sparsity
pattern. In particular, we apply a log(P)-level nested dissection followe
d by AMD (approximate minimum degree) ordering at the leaf level, where P
is the number of threads. This ordering naturally leads to a parallel meth
od. Results show that our preconditioner outperformed standard incomplete
Cholesky preconditioner with much less iterations and scaled up to 64 thre
ads on a multicore CPU. Our poster has three major parts: the randomized s
ampling algorithm, the parallel algorithm/implementation, and results on p
arallel scalability as well as comparison to incomplete Cholesky.\n\nTag:
Student Program\n\nRegistration Category: Tech Program Reg Pass, Exhibits
Reg Pass
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