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Title: Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs

Abstract

Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient smoother algorithms suitable for current and evolving GPU and multicore CPU systems is a significant challenge. We address this issue in the case of constant-coefficient stencils arising in the solution of elliptic partial differential equations on structured 3D uniform and adaptively refined block structured grids. Robust, highly parallel implementations of block Jacobi and chaotic block Gauss-Seidel algorithms with exact inversion of the blocks are developed using different parallelization techniques. Experimental results for NVIDIA Fermi/Kepler GPUs and AMD multicore systems are presented.

Authors:
 [1];  [1];  [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1134156
Report Number(s):
ORNL/TM-2014/225
KJ0403000; ERKJR04
DOE Contract Number:  
DE-AC05-00OR22725
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English

Citation Formats

Philip, Bobby, Wang, Zhen, and Berrill, Mark A. Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs. United States: N. p., 2014. Web. doi:10.2172/1134156.
Philip, Bobby, Wang, Zhen, & Berrill, Mark A. Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs. United States. https://doi.org/10.2172/1134156
Philip, Bobby, Wang, Zhen, and Berrill, Mark A. Sun . "Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs". United States. https://doi.org/10.2172/1134156.
@article{osti_1134156,
title = {Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs},
author = {Philip, Bobby and Wang, Zhen and Berrill, Mark A},
abstractNote = {Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient smoother algorithms suitable for current and evolving GPU and multicore CPU systems is a significant challenge. We address this issue in the case of constant-coefficient stencils arising in the solution of elliptic partial differential equations on structured 3D uniform and adaptively refined block structured grids. Robust, highly parallel implementations of block Jacobi and chaotic block Gauss-Seidel algorithms with exact inversion of the blocks are developed using different parallelization techniques. Experimental results for NVIDIA Fermi/Kepler GPUs and AMD multicore systems are presented.},
doi = {10.2172/1134156},
url = {https://www.osti.gov/biblio/1134156}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2014},
month = {6}
}

Technical Report:
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