BoomerAMG 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; PCBDDC; MFEM; CUDA; ILUT; METIS; PyAMG; SLEPc; libMesh; deal.ii; SuperLU; CPR-AMG Cited in: 207 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Zbl 0995.65128Henson, Van Emden; Meier Yang, Ulrike 2002 all top 5 Cited by 463 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 363 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. 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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 all top 5 Cited in 24 Fields 176 Numerical analysis (65-XX) 62 Fluid mechanics (76-XX) 44 Partial differential equations (35-XX) 25 Mechanics of deformable solids (74-XX) 15 Biology and other natural sciences (92-XX) 10 Optics, electromagnetic theory (78-XX) 9 Geophysics (86-XX) 7 Computer science (68-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Integral equations (45-XX) 1 History and biography (01-XX) 1 Potential theory (31-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year