Strategy for fine-grained parallelism in multi-level computational engineering solvers

Stephen L. Wood; Chad E. Burdyshaw; J. Taylor Erwin; Douglas Stefanski; Ryan Glasby; Gregory Peterson

doi:10.2514/6.2018-0397

Strategy for fine-grained parallelism in multi-level computational engineering solvers

Stephen L. Wood, Chad E. Burdyshaw, J. Taylor Erwin, Douglas Stefanski, Ryan Glasby, Gregory Peterson

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

A strategy to harness fine-grained parallelism for linear solvers within computational tools that operate on distributed domains is presented. “MPI + X” is the industry term for multilevel parallelism. “MPI” refers to the component coordinating inter-node communication via message passing. Within this article we focus our attention on the “X”, the on-node component that utilizes fine-grained parallelism in shared memory. In this work, “X” is OpenMP® on Intel® Xeon® Phi™ Knight’s Landing and Intel® Xeon® Skylake processors, and “X” is CUDA® 9 on a NVIDIA® Tesla® P100 GPU accelerator. The strategy is applied to the right preconditioned GMRES method to explore two pairs of algorithmic alternatives, 1) preconditioner generation by Gaussian Elimination or PariLU algorithms, and 2) orthonormalization of a Krylov subspace by the commonly used modified Gram-Schmidt Arnoldi or the Householder Transformation Arnoldi processes. Particular emphasis is placed on the implications of parallelism on numerical qualities of the solution process. Preconditioning GMRES with factorizations generated by the PariLU algorithm is found to effectively accelerate convergence for some poorly conditioned linear systems. Orthonormalizing a GMRES Krylov subspace with the Householder Transformation Arnoldi processes is found to match or surpass the convergence rate achieved utilizing the modified Gram-Schmidt Arnoldi process when searching for approximate solutions to 10 linear systems from modern computational engineering applications.

Original language	English
Title of host publication	AIAA Information Systems-AIAA Infotech at Aerospace
Publisher	American Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)	9781624105272
DOIs	https://doi.org/10.2514/6.2018-0397
State	Published - Jan 1 2018
Externally published	Yes
Event	AIAA Information Systems-AIAA Infotech at Aerospace, 2018 - Kissimmee, United States Duration: Jan 8 2018 → Jan 12 2018

Publication series

Name	AIAA Information Systems-AIAA Infotech at Aerospace, 2018

Conference

Conference	AIAA Information Systems-AIAA Infotech at Aerospace, 2018
Country/Territory	United States
City	Kissimmee
Period	01/8/18 → 01/12/18

Funding

The Co-design Approach for Advances in Software and Hardware (CoDAASH) project focuses on understanding the relationship between algorithms and hardware platforms and how to jointly optimize the software and hardware in order to achieve efficient implementations for applications in materials science, chemistry, and physics. CoDAASH is a joint effort between the University of Tennessee, Knoxville; Iowa State University; University of Texas, El Paso; and the University of California, San Diego; and is funded by the United States Air Force Office of Scientific Research (AFOSR). This material is based upon work supported by the AFOSR under Award No. FA9550-12-1-0476.

Funders	Funder number
University of Texas
Air Force Office of Scientific Research	FA9550-12-1-0476
University of Tennessee
University of California, San Diego

Access to Document

10.2514/6.2018-0397

Cite this

Wood, S. L., Burdyshaw, C. E., Erwin, J. T., Stefanski, D., Glasby, R., & Peterson, G. (2018). Strategy for fine-grained parallelism in multi-level computational engineering solvers. In AIAA Information Systems-AIAA Infotech at Aerospace (AIAA Information Systems-AIAA Infotech at Aerospace, 2018). American Institute of Aeronautics and Astronautics Inc, AIAA. https://doi.org/10.2514/6.2018-0397

@inproceedings{4b5ccc858eeb43dba545a260fa9e71a1,

title = "Strategy for fine-grained parallelism in multi-level computational engineering solvers",

abstract = "A strategy to harness fine-grained parallelism for linear solvers within computational tools that operate on distributed domains is presented. “MPI + X” is the industry term for multilevel parallelism. “MPI” refers to the component coordinating inter-node communication via message passing. Within this article we focus our attention on the “X”, the on-node component that utilizes fine-grained parallelism in shared memory. In this work, “X” is OpenMP{\textregistered} on Intel{\textregistered} Xeon{\textregistered} Phi{\texttrademark} Knight{\textquoteright}s Landing and Intel{\textregistered} Xeon{\textregistered} Skylake processors, and “X” is CUDA{\textregistered} 9 on a NVIDIA{\textregistered} Tesla{\textregistered} P100 GPU accelerator. The strategy is applied to the right preconditioned GMRES method to explore two pairs of algorithmic alternatives, 1) preconditioner generation by Gaussian Elimination or PariLU algorithms, and 2) orthonormalization of a Krylov subspace by the commonly used modified Gram-Schmidt Arnoldi or the Householder Transformation Arnoldi processes. Particular emphasis is placed on the implications of parallelism on numerical qualities of the solution process. Preconditioning GMRES with factorizations generated by the PariLU algorithm is found to effectively accelerate convergence for some poorly conditioned linear systems. Orthonormalizing a GMRES Krylov subspace with the Householder Transformation Arnoldi processes is found to match or surpass the convergence rate achieved utilizing the modified Gram-Schmidt Arnoldi process when searching for approximate solutions to 10 linear systems from modern computational engineering applications.",

author = "Wood, {Stephen L.} and Burdyshaw, {Chad E.} and Erwin, {J. Taylor} and Douglas Stefanski and Ryan Glasby and Gregory Peterson",

note = "Publisher Copyright: {\textcopyright} 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.; AIAA Information Systems-AIAA Infotech at Aerospace, 2018 ; Conference date: 08-01-2018 Through 12-01-2018",

year = "2018",

month = jan,

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doi = "10.2514/6.2018-0397",

language = "English",

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Wood, SL, Burdyshaw, CE, Erwin, JT, Stefanski, D, Glasby, R & Peterson, G 2018, Strategy for fine-grained parallelism in multi-level computational engineering solvers. in AIAA Information Systems-AIAA Infotech at Aerospace. AIAA Information Systems-AIAA Infotech at Aerospace, 2018, American Institute of Aeronautics and Astronautics Inc, AIAA, AIAA Information Systems-AIAA Infotech at Aerospace, 2018, Kissimmee, United States, 01/8/18. https://doi.org/10.2514/6.2018-0397

Strategy for fine-grained parallelism in multi-level computational engineering solvers. / Wood, Stephen L.; Burdyshaw, Chad E.; Erwin, J. Taylor et al.
AIAA Information Systems-AIAA Infotech at Aerospace. American Institute of Aeronautics and Astronautics Inc, AIAA, 2018. (AIAA Information Systems-AIAA Infotech at Aerospace, 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - A strategy to harness fine-grained parallelism for linear solvers within computational tools that operate on distributed domains is presented. “MPI + X” is the industry term for multilevel parallelism. “MPI” refers to the component coordinating inter-node communication via message passing. Within this article we focus our attention on the “X”, the on-node component that utilizes fine-grained parallelism in shared memory. In this work, “X” is OpenMP® on Intel® Xeon® Phi™ Knight’s Landing and Intel® Xeon® Skylake processors, and “X” is CUDA® 9 on a NVIDIA® Tesla® P100 GPU accelerator. The strategy is applied to the right preconditioned GMRES method to explore two pairs of algorithmic alternatives, 1) preconditioner generation by Gaussian Elimination or PariLU algorithms, and 2) orthonormalization of a Krylov subspace by the commonly used modified Gram-Schmidt Arnoldi or the Householder Transformation Arnoldi processes. Particular emphasis is placed on the implications of parallelism on numerical qualities of the solution process. Preconditioning GMRES with factorizations generated by the PariLU algorithm is found to effectively accelerate convergence for some poorly conditioned linear systems. Orthonormalizing a GMRES Krylov subspace with the Householder Transformation Arnoldi processes is found to match or surpass the convergence rate achieved utilizing the modified Gram-Schmidt Arnoldi process when searching for approximate solutions to 10 linear systems from modern computational engineering applications.

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Strategy for fine-grained parallelism in multi-level computational engineering solvers

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