Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution

Reisner, Andrew; Olson, Luke N.; Moulton, J. David

doi:10.1137/17M1146440

Title: Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution

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Abstract

The effcient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for common discretizations makes them a good candidate for an efficient parallel solver. Yet, modern architectures for high-performance computing systems continue to challenge the parallel scalability of multilevel solvers. While algebraic multigrid methods are robust for solving a variety of problems, the increasing importance of data locality and cost of data movement in modern architectures motivates the need to carefully exploit structure in the problem. Robust logically structured variational multigrid methods, such as Black Box Multigrid (BoxMG), maintain structure throughout the multigrid hierarchy. This avoids indirection and increased coarse- grid communication costs typical in parallel algebraic multigrid. Nevertheless, the parallel scalability of structured multigrid is challenged by coarse-grid problems where the overhead in communication dominates computation. In this paper, an algorithm is introduced for redistributing coarse-grid problems through incremental agglomeration. Guided by a predictive performance model, this algorithm provides robust redistribution decisions for structured multilevel solvers. A two-dimensional diffusion problem is used to demonstrate the significant gain in performance of this algorithm over the previous approach that used agglomeration tomore »« less

Authors:

Reisner, Andrew ^[1]; Olson, Luke N. ^[2]; Moulton, J. David ^[2]

Univ. of Illinois, Urbana-Champaign, IL (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Tue Jul 17 00:00:00 EDT 2018

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1463543

Report Number(s):: LA-UR-17-22886
Journal ID: ISSN 1064-8275

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing

Additional Journal Information:: Journal Volume: 40; Journal Issue: 4; Journal ID: ISSN 1064-8275

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Mathematics; multigrid, structure, parallel, scalability, stencil

Citation Formats


                    Reisner, Andrew, Olson, Luke N., and Moulton, J. David. Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution.  United States: N. p., 2018. 
Web.  doi:10.1137/17M1146440.

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                    Reisner, Andrew, Olson, Luke N., & Moulton, J. David. Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution.  United States.  https://doi.org/10.1137/17M1146440

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                    Reisner, Andrew, Olson, Luke N., and Moulton, J. David. Tue .  
"Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution".  United States.  https://doi.org/10.1137/17M1146440.  https://www.osti.gov/servlets/purl/1463543.

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@article{osti_1463543,

  title        = {Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution},

  author       = {Reisner, Andrew and Olson, Luke N. and Moulton, J. David},

  abstractNote = {The effcient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for common discretizations makes them a good candidate for an efficient parallel solver. Yet, modern architectures for high-performance computing systems continue to challenge the parallel scalability of multilevel solvers. While algebraic multigrid methods are robust for solving a variety of problems, the increasing importance of data locality and cost of data movement in modern architectures motivates the need to carefully exploit structure in the problem. Robust logically structured variational multigrid methods, such as Black Box Multigrid (BoxMG), maintain structure throughout the multigrid hierarchy. This avoids indirection and increased coarse- grid communication costs typical in parallel algebraic multigrid. Nevertheless, the parallel scalability of structured multigrid is challenged by coarse-grid problems where the overhead in communication dominates computation. In this paper, an algorithm is introduced for redistributing coarse-grid problems through incremental agglomeration. Guided by a predictive performance model, this algorithm provides robust redistribution decisions for structured multilevel solvers. A two-dimensional diffusion problem is used to demonstrate the significant gain in performance of this algorithm over the previous approach that used agglomeration to one processor. In addition, the parallel scalability of this approach},

  doi          = {10.1137/17M1146440},

  journal      = {SIAM Journal on Scientific Computing},

  number       = 4,

  volume       = 40,

  place        = {United States},

  year         = {Tue Jul 17 00:00:00 EDT 2018},

  month        = {Tue Jul 17 00:00:00 EDT 2018}

}

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