swMATH ID: 86
Software Authors: Henson, Van Emden; Meier Yang, Ulrike
Description: BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Driven by the need to solve linear systems arising from problems posed on extremely large, unstructured grids, there has been a recent resurgence of interest in algebraic multigrid (AMG). AMG is attractive in that it holds out the possibility of multigrid-like performance on unstructured grids. The sheer size of many modern physics and simulation problems has led to the development of massively parallel computers, and has sparked much research into developing algorithms for them. Parallelizing AMG is a difficult task, however. While much of the AMG method parallelizes readily, the process of coarse-grid selection, in particular, is fundamentally sequential in nature. We have previously introduced a parallel algorithm [cf. A. J. Cleary, R. D. Falgout, V. E. Henson and J. E. Jones, Coarse grid selection for parallel algebraic multigrid, in: A. Ferriera, J. Rollin, H. Simon, S.-H. Teng (eds.), Proceedings of the Fifth International Symposium on Solving Irregularly Structured Problems in Parallel, Lecture Notes in Computer Science, Vol. 1457, Springer, New York (1998)] for the selection of coarse-grid points, based on modifications of certain parallel independent set algorithms and the application of heuristic designed to insure the quality of the coarse grids, and shown results from a prototype serial version of the algorithm. In this paper we describe an implementation of a parallel AMG code, using the algorithm of A. J. Cleary, R. D. Falgout and V. E. Henson [loc. cit.] as well as other approaches to parallelizing the coarse-grid selection. We consider three basic coarsening schemes and certain modifications to the basic schemes, designed to address specific performance issues. We present numerical results for a broad range of problem sizes and descriptions, and draw conclusion regarding the efficacy of the method. Finally, we indicate the current directions of the research.
Homepage: http://www.sciencedirect.com/science/article/pii/S0168927401001155
Programming Languages: C
Keywords: Laplace equation; finite difference method; preconditioning; algebraic multigrid; parallel computing; unstructured grids; algorithms; numerical results
Related Software: hypre; PETSc; ML; MUMPS; Trilinos; FEniCS; Gmsh; SparseMatrix; IPARS; MFEM; PCBDDC; CUDA; ILUT; METIS; PyAMG; libMesh; SLEPc; deal.ii; SuperLU; CPR-AMG
Cited in: 207 Publications
all top 5

Cited by 462 Authors

10 Klawonn, Axel
10 Rheinbach, Oliver
9 Lanser, Martin
8 Vassilevski, Panayot Spirov
7 Meier Yang, Ulrike
7 Shu, Shi
6 Kolev, Tzanio V.
6 Manteuffel, Thomas A.
6 Olson, Luke N.
6 Plank, Gernot
6 Xu, Xiaowen
5 D’Ambra, Pasqua
5 Falgout, Robert D.
5 MacLachlan, Scott P.
5 Scacchi, Simone
5 Yue, Xiaoqiang
4 Augustin, Christoph M.
4 Filippone, Salvatore
4 Lee, Chak Shing
4 Li, Lingxiao
4 Rhebergen, Sander
4 Ruge, John W.
4 Wathen, Andrew John
4 Wells, Garth N.
4 Xu, Jinchao
4 Zheng, Weiying
3 Bui, Quan M.
3 Cai, Xiao-Chuan
3 Castelletto, Nicola
3 Chen, Zhangxin
3 di Serafino, Daniela
3 Emans, Maximilian
3 Jönsthövel, Tom B.
3 Keyes, David Elliot
3 Liu, Hui
3 Liu, Lulu
3 Luo, Li
3 Martineau, Richard C.
3 McCormick, Steve Fahrney
3 Napov, Artem
3 Notay, Yvan
3 Pavarino, Luca Franco
3 Scheichl, Robert
3 Southworth, Ben S.
3 Wang, Yaqi
3 White, Joshua A.
2 Adler, James H.
2 An, Hengbin
2 Ananthan, Shreyas
2 Baker, Allison H.
2 Barker, Andrew T.
2 Brown, Jed
2 Dalcín, Lisandro D.
2 De Sterck, Hans
2 DeHart, Mark D.
2 Dobrev, Veselin A.
2 Fu, Guosheng
2 Gerritsen, Margot G.
2 Gsell, Matthias A. F.
2 Haase, Gundolf
2 Hamon, François P.
2 Heil, Matthias
2 Hu, Xiaozhe
2 Iaccarino, Gianluca
2 Jolivet, Pierre
2 Karabelas, Elias
2 Kong, Fande
2 Kosturski, Nikola
2 Kunisch, Karl
2 Lambers, James V.
2 Lemon, Christopher
2 Logg, Anders
2 Maddison, James R.
2 Manguoglu, Murat
2 Margenov, Svetozar D.
2 Masson, Roland
2 Moncorgé, Arthur
2 Møyner, Olav
2 Neic, Aurel
2 Neumüller, Martin
2 Osei-Kuffuor, Daniel
2 Pain, Christopher C.
2 Pazner, Will E.
2 Permann, Cody J.
2 Roy, Thomas
2 Saad, Yousef
2 Salinas, Pablo
2 Schroder, Jacob B.
2 Schunert, Sebastian
2 Uran, Matthias
2 Vutov, Yavor
2 Wang, Kun
2 Wang, Libo
2 Wang, Xiaoping
2 Weber, Janine
2 Xiao, Yingxiong
2 Xu, Xinhai
2 Yang, Ulrike M.
2 Yang, Xuejun
2 Ye, Shuai
...and 362 more Authors
all top 5

Cited in 46 Serials

49 SIAM Journal on Scientific Computing
33 Journal of Computational Physics
16 Numerical Linear Algebra with Applications
11 Computer Methods in Applied Mechanics and Engineering
6 Computational Geosciences
5 Computational Mechanics
5 Journal of Scientific Computing
5 ETNA. Electronic Transactions on Numerical Analysis
4 Journal of Computational and Applied Mathematics
4 Applied Numerical Mathematics
3 Computers and Fluids
3 Computers & Mathematics with Applications
3 International Journal for Numerical Methods in Engineering
3 Communications in Computational Physics
2 ACM Transactions on Mathematical Software
2 Applied Mathematics and Computation
2 SIAM Journal on Numerical Analysis
2 SIAM Journal on Matrix Analysis and Applications
2 Numerical Algorithms
2 Applied Mathematical Modelling
2 East Asian Journal on Applied Mathematics
1 Computer Physics Communications
1 International Journal for Numerical Methods in Fluids
1 Journal of Fluid Mechanics
1 Journal of Mathematical Biology
1 Computing
1 Numerische Mathematik
1 Computer Aided Geometric Design
1 Parallel Computing
1 Computational Mathematics and Mathematical Physics
1 International Journal of Computer Mathematics
1 Communications in Numerical Methods in Engineering
1 Computing and Visualization in Science
1 Lobachevskii Journal of Mathematics
1 Archives of Computational Methods in Engineering
1 Journal of Applied Mathematics
1 Multiscale Modeling & Simulation
1 International Journal of Computational Methods
1 Acta Numerica
1 Acta Mechanica Sinica
1 Advanced Modeling and Optimization
1 SIAM Journal on Imaging Sciences
1 Discrete and Continuous Dynamical Systems. Series S
1 ISRN Applied Mathematics
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys
1 Communications on Applied Mathematics and Computation

Citations by Year