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Title: Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

Abstract

ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.

Authors:
 [1];  [1];  [1];  [1];  [1];  [1]
  1. LLNL
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1418985
Report Number(s):
ParELAG; 005578MLTPL00
LLNL-CODE-745557
DOE Contract Number:
AC52-07NA27344
Resource Type:
Software
Software Revision:
00
Software Package Number:
005578
Software CPU:
MLTPL
Open Source:
Yes
Source Code Available:
Yes
Country of Publication:
United States

Citation Formats

Barker, Andrew T., Benson, Thomas R., Lee, Chak Shing, Osborn, Sarah V., Vassilevski, Panayot S., and Villa, Umberto E.. Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library. Computer software. https://www.osti.gov//servlets/purl/1418985. Vers. 00. USDOE National Nuclear Security Administration (NNSA). 24 Oct. 2017. Web.
Barker, Andrew T., Benson, Thomas R., Lee, Chak Shing, Osborn, Sarah V., Vassilevski, Panayot S., & Villa, Umberto E.. (2017, October 24). Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library (Version 00) [Computer software]. https://www.osti.gov//servlets/purl/1418985.
Barker, Andrew T., Benson, Thomas R., Lee, Chak Shing, Osborn, Sarah V., Vassilevski, Panayot S., and Villa, Umberto E.. Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library. Computer software. Version 00. October 24, 2017. https://www.osti.gov//servlets/purl/1418985.
@misc{osti_1418985,
title = {Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library, Version 00},
author = {Barker, Andrew T. and Benson, Thomas R. and Lee, Chak Shing and Osborn, Sarah V. and Vassilevski, Panayot S. and Villa, Umberto E.},
abstractNote = {ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.},
url = {https://www.osti.gov//servlets/purl/1418985},
doi = {},
year = 2017,
month = ,
note =
}

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  • ParFELAG is a parallel distributed memory C++ library for numerical upscaling of finite element discretizations. It provides optimal complesity algorithms ro build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured mesh (under the assumption that the topology of the agglomerated entities is correct). Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.
  • The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG) To date, however, no parallel AMG algorithms exist We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifications of certain paallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids A prototype serial version of the algorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity
  • The development of high performance, massively parallel computers and the increasing demands of computationally challenging applications have necessitated the development of scalable solvers and preconditioners. One of the most effective ways to achieve scalability is the use of multigrid or multilevel techniques. Algebraic multigrid (AMG) is a very efficient algorithm for solving large problems on unstructured grids. While much of it can be parallelized in a straightforward way, some components of the classical algorithm, particularly the coarsening process and some of the most efficient smoothers, are highly sequential, and require new parallel approaches. This chapter presents the basic principles ofmore » AMG and gives an overview of various parallel implementations of AMG, including descriptions of parallel coarsening schemes and smoothers, some numerical results as well as references to existing software packages.« less

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