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Title: A Hierarchical Low-rank Solver for Sparse Linear Systems.

Abstract

Abstract not provided.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1426632
Report Number(s):
SAND2017-2694C
651673
DOE Contract Number:
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: Proposed for presentation at the Householder Symposium held June 18-23, 2017 in Blacksburg, VA.
Country of Publication:
United States
Language:
English

Citation Formats

Boman, Erik G., Chao Chen, Eric Darve, Hadi Pouransari, and Rajamanickam, Sivasankaran. A Hierarchical Low-rank Solver for Sparse Linear Systems.. United States: N. p., 2017. Web.
Boman, Erik G., Chao Chen, Eric Darve, Hadi Pouransari, & Rajamanickam, Sivasankaran. A Hierarchical Low-rank Solver for Sparse Linear Systems.. United States.
Boman, Erik G., Chao Chen, Eric Darve, Hadi Pouransari, and Rajamanickam, Sivasankaran. Wed . "A Hierarchical Low-rank Solver for Sparse Linear Systems.". United States. doi:. https://www.osti.gov/servlets/purl/1426632.
@article{osti_1426632,
title = {A Hierarchical Low-rank Solver for Sparse Linear Systems.},
author = {Boman, Erik G. and Chao Chen and Eric Darve and Hadi Pouransari and Rajamanickam, Sivasankaran},
abstractNote = {Abstract not provided.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}

Conference:
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  • 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 everymore » processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.« less
  • Abstract not provided.
  • An easily and efficiently parallelizable direct method is given for solving a block linear system Bx = y, where B = D + Q is the sum of a non-singular block diagonal matrix D and a matrix Q with low-rank blocks. This implicitly defines a new preconditioning method with an operation count close to the cost of calculating a matrix-vector product Qw for some w, plus at most twice the cost of calculating Qw for some w. When implemented on a parallel machine the processor utilization can be as good as that of those operations. Order estimates are given formore » the general case, and an implementation is compared to block SSOR preconditioning.« less
  • Abstract not provided.
  • We explore a coarse grain parallel algorithm for the solution of large sparse linear systems with symmetric positive definite matrix, based on a preconditioned conjugate gradient method.