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Title: Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

Abstract

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented on both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.

Authors:
 [1];  [1];  [1];  [1];  [1]
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  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1237520
Report Number(s):
SAND-2016-0637R
619072
DOE Contract Number:
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; sparse factorization; algorithm-by-block; 2D layout; task parallelism

Citation Formats

Kim, Kyungjoo, Rajamanickam, Sivasankaran, Stelle, George Widgery, Edwards, Harold C., and Olivier, Stephen Lecler. Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout. United States: N. p., 2016. Web. doi:10.2172/1237520.
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Kim, Kyungjoo, Rajamanickam, Sivasankaran, Stelle, George Widgery, Edwards, Harold C., & Olivier, Stephen Lecler. Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout. United States. doi:10.2172/1237520.
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Kim, Kyungjoo, Rajamanickam, Sivasankaran, Stelle, George Widgery, Edwards, Harold C., and Olivier, Stephen Lecler. Fri . "Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout". United States. doi:10.2172/1237520. https://www.osti.gov/servlets/purl/1237520.
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@article{osti_1237520,
title = {Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout},
author = {Kim, Kyungjoo and Rajamanickam, Sivasankaran and Stelle, George Widgery and Edwards, Harold C. and Olivier, Stephen Lecler},
abstractNote = {We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented on both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.},
doi = {10.2172/1237520},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 2016},
month = {Fri Jan 01 00:00:00 EST 2016}
}
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DOI:  10.2172/1237520
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