A New Semistructured Algebraic Multigrid Method

Magri, Victor P.; Falgout, Robert D.; Yang, Ulrike M.

doi:10.1137/21m1434118

Title: A New Semistructured Algebraic Multigrid Method

Journal Article · Thu Jun 29 00:00:00 EDT 2023 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/21m1434118· OSTI ID:2202928

^[1]; Falgout, Robert D. ^[1]; Yang, Ulrike M. ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display good parallelization properties. Since current architecture trends are favoring regular compute patterns to achieve high performance, the ability to express structure has become much more important. The hypre software library provides high-performance multigrid preconditioners and solvers through conceptual interfaces, including a semistructured interface that describes matrices primarily in terms of stencils and logically structured grids. This paper presents a new semistructured algebraic multigrid (SSAMG) method built on this interface. The numerical convergence and performance of a CPU implementation of this method are evaluated for a set of semistructured problems. In conclusion, SSAMG achieves significantly better setup times than hypre’s unstructured AMG solvers and comparable convergence. In addition, the new method is capable of solving more complex problems than hypre’s structured solvers.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2202928

Report Number(s):: LLNL-JRNL-824519; 1038066

Journal Information:: SIAM Journal on Scientific Computing, Vol. 45, Issue 3; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

References (28)

A Multigrid Tutorial, Second Edition Briggs, William L.; Henson, Van Emden; McCormick, Steve F. Other Titles in Applied Mathematics https://doi.org/10.1137/1.9780898719505	book	January 2000
Hierarchical hybrid grids: data structures and core algorithms for multigrid Bergen, Benjamin Karl; Hülsemann, Frank Numerical Linear Algebra with Applications, Vol. 11, Issue 2-3 https://doi.org/10.1002/nla.382	journal	March 2004
Hierarchical hybrid grids: achieving TERAFLOP performance on large scale finite element simulations Bergen, B.; Wellein, G.; Hülsemann, F. International Journal of Parallel, Emergent and Distributed Systems, Vol. 22, Issue 4 https://doi.org/10.1080/17445760701442218	journal	August 2007
The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners Falgout, Robert D.; Jones, Jim E.; Yang, Ulrike Meier Lecture Notes in Computational Science and Engineering https://doi.org/10.1007/3-540-31619-1_8	book	January 2006
Semicoarsening Multigrid on Distributed Memory Machines Brown, Peter N.; Falgout, Robert D.; Jones, Jim E. SIAM Journal on Scientific Computing, Vol. 21, Issue 5 https://doi.org/10.1137/S1064827598339141	journal	January 2000
Multigrid Methods on Semi-Structured Grids Rodrigo, Carmen; Gaspar, Francisco J.; Lisbona, Francisco J. Archives of Computational Methods in Engineering, Vol. 19, Issue 4 https://doi.org/10.1007/s11831-012-9078-9	journal	October 2012
Conceptual interfaces in hypre Falgout, Robert D.; Jones, Jim E.; Yang, Ulrike Meier Future Generation Computer Systems, Vol. 22, Issue 1-2 https://doi.org/10.1016/j.future.2003.09.006	journal	January 2006
Massively parallel finite difference elasticity using block-structured adaptive mesh refinement with a geometric multigrid solver Runnels, Brandon; Agrawal, Vinamra; Zhang, Weiqun Journal of Computational Physics, Vol. 427 https://doi.org/10.1016/j.jcp.2020.110065	journal	February 2021
Adaptive mesh, finite volume modeling of marine ice sheets Cornford, Stephen L.; Martin, Daniel F.; Graves, Daniel T. Journal of Computational Physics, Vol. 232, Issue 1 https://doi.org/10.1016/j.jcp.2012.08.037	journal	January 2013
Multigrid Smoothers for Ultraparallel Computing Baker, Allison H.; Falgout, Robert D.; Kolev, Tzanio V. SIAM Journal on Scientific Computing, Vol. 33, Issue 5 https://doi.org/10.1137/100798806	journal	January 2011
BoomerAMG: A parallel algebraic multigrid solver and preconditioner Henson, Van Emden; Yang, Ulrike Meier Applied Numerical Mathematics, Vol. 41, Issue 1 https://doi.org/10.1016/S0168-9274(01)00115-5	journal	April 2002
Reducing Complexity in Parallel Algebraic Multigrid Preconditioners De Sterck, Hans; Yang, Ulrike Meier; Heys, Jeffrey J. SIAM Journal on Matrix Analysis and Applications, Vol. 27, Issue 4 https://doi.org/10.1137/040615729	journal	January 2006
Stencil computations for PDE-based applications with examples from DUNE and hypre: Stencil Computations for PDE-based Applications Engwer, C.; Falgout, R. D.; Yang, U. M. Concurrency and Computation: Practice and Experience, Vol. 29, Issue 17 https://doi.org/10.1002/cpe.4097	journal	February 2017
AMReX: a framework for block-structured adaptive mesh refinement Zhang, Weiqun; Almgren, Ann; Beckner, Vince Journal of Open Source Software, Vol. 4, Issue 37 https://doi.org/10.21105/joss.01370	journal	May 2019
Towards Textbook Efficiency for Parallel Multigrid Gmeiner, Björn; Rüde, Ulrich; Stengel, Holger Numerical Mathematics: Theory, Methods and Applications, Vol. 8, Issue 1 https://doi.org/10.4208/nmtma.2015.w10si	journal	February 2015
Scaling Hypre’s Multigrid Solvers to 100,000 Cores Baker, Allison H.; Falgout, Robert D.; Kolev, Tzanio V. High-Performance Scientific Computing https://doi.org/10.1007/978-1-4471-2437-5_13	book	January 2012
Porting hypre to heterogeneous computer architectures: Strategies and experiences Falgout, Robert D.; Li, Ruipeng; Sjögreen, Björn Parallel Computing, Vol. 108 https://doi.org/10.1016/j.parco.2021.102840	journal	December 2021
Peta-Scale Hierarchical Hybrid Multigrid Using Hybrid Parallelization Gmeiner, Björn; Rüde, Ulrich Large-Scale Scientific Computing https://doi.org/10.1007/978-3-662-43880-0_50	book	January 2014
AMReX: Block-structured adaptive mesh refinement for multiphysics applications Zhang, Weiqun; Myers, Andrew; Gott, Kevin The International Journal of High Performance Computing Applications https://doi.org/10.1177/10943420211022811	journal	June 2021
A Parallel Multigrid Preconditioned Conjugate Gradient Algorithm for Groundwater Flow Simulations Ashby, Steven F.; Falgout, Robert D. Nuclear Science and Engineering, Vol. 124, Issue 1 https://doi.org/10.13182/NSE96-A24230	journal	September 1996
A New Class of AMG Interpolation Methods Based on Matrix-Matrix Multiplications Li, Ruipeng; Sjögreen, Björn; Yang, Ulrike Meier SIAM Journal on Scientific Computing https://doi.org/10.1137/20M134931X	journal	July 2021
Adaptive mesh refinement with an enhanced velocity mixed finite element method on semi-structured grids using a fully coupled solver Ganis, Benjamin; Pencheva, Gergina; Wheeler, Mary F. Computational Geosciences, Vol. 23, Issue 1 https://doi.org/10.1007/s10596-018-9789-6	journal	October 2018
Managing application complexity in the SAMRAI object-oriented framework Hornung, Richard D.; Kohn, Scott R. Concurrency and Computation: Practice and Experience, Vol. 14, Issue 5 https://doi.org/10.1002/cpe.652	journal	January 2002
LFRic: Meeting the challenges of scalability and performance portability in Weather and Climate models Adams, S. V.; Ford, R. W.; Hambley, M. Journal of Parallel and Distributed Computing, Vol. 132 https://doi.org/10.1016/j.jpdc.2019.02.007	journal	October 2019
A review of algebraic multigrid Stüben, K. Journal of Computational and Applied Mathematics, Vol. 128, Issue 1-2 https://doi.org/10.1016/S0377-0427(00)00516-1	journal	March 2001
Textbook Efficiency: Massively Parallel Matrix-Free Multigrid for the Stokes System Kohl, Nils; Rüde, Ulrich SIAM Journal on Scientific Computing, Vol. 44, Issue 2 https://doi.org/10.1137/20M1376005	journal	April 2022
NonInvasive Multigrid For SemiStructured Grids Mayr, Matthias; Berger-Vergiat, Luc; Ohm, Peter SIAM Journal on Scientific Computing, Vol. 44, Issue 4 https://doi.org/10.1137/20M1375413	journal	August 2022
On long-range interpolation operators for aggressive coarsening: INTERPOLATION FOR AGGRESSIVE COARSENING Yang, Ulrike Meier Numerical Linear Algebra with Applications, Vol. 17, Issue 2-3 https://doi.org/10.1002/nla.689	journal	December 2009

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97 MATHEMATICS AND COMPUTING
algebraic multigrid
semistructured multigrid
semistructured grids
structured adaptive mesh refinement

Title: A New Semistructured Algebraic Multigrid Method

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