Algebraic multigrid theory: The symmetric case
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
A parallel graph coloring heuristic
SIAM Journal on Scientific Computing
Robustness and Scalability of Algebraic Multigrid
SIAM Journal on Scientific Computing
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
Algebraic Multigrid Based on Element Interpolation (AMGe)
SIAM Journal on Scientific Computing
Coarse-Grid Selection for Parallel Algebraic Multigrid
IRREGULAR '98 Proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel
A distributed memory unstructured gauss-seidel algorithm for multigrid smoothers
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Comparing the Performance of Solvers for a Bioelectric Field Problem
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Pursuing scalability for hypre's conceptual interfaces
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Is 1.7 x 10^10 Unknowns the Largest Finite Element System that Can Be Solved Today?
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Conceptual interfaces in hypre
Future Generation Computer Systems
Journal of Computational Physics
An object-oriented framework for the development of scalable parallel multilevel preconditioners
ACM Transactions on Mathematical Software (TOMS)
Compatible coarsening in the multigraph algorithm
Advances in Engineering Software
Relaxed RS0 or CLJP coarsening strategy for parallel AMG
Parallel Computing
On the development of PSBLAS-based parallel two-level Schwarz preconditioners
Applied Numerical Mathematics
Short Note: On preconditioning for a parallel solution of the Richards equation
Computers & Geosciences
Dendro: parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Fast and robust solvers for pressure-correction in bubbly flow problems
Journal of Computational Physics
A Parallel Implementation of the Trace Minimization Eigensolver
High Performance Computing for Computational Science - VECPAR 2008
Parallel Eigensolvers for a Discretized Radiative Transfer Problem
High Performance Computing for Computational Science - VECPAR 2008
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method
Journal of Computational Physics
Graph partitioning and disturbed diffusion
Parallel Computing
Scalable temporal order analysis for large scale debugging
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Conceptual interfaces in hypre
Future Generation Computer Systems
Estimating the Laplace-Beltrami operator by restricting 3D functions
SGP '09 Proceedings of the Symposium on Geometry Processing
Journal of Computational Physics
ACM Transactions on Mathematical Software (TOMS)
Finite element modeling of the deformation of magnetoelastic film
Journal of Computational Physics
Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D
Journal of Scientific Computing
Characterizing the Influence of System Noise on Large-Scale Applications by Simulation
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Aggregation AMG for distributed systems suffering from large message numbers
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
AMG for linear systems in engine flow simulations
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Accelerating shape optimizing load balancing for parallel fem simulations by algebraic multigrid
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Towards using and improving the NAS parallel benchmarks: a parallel patterns approach
Proceedings of the 2010 Workshop on Parallel Programming Patterns
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Efficient Parallel AMG Methods for Approximate Solutions of Linear Systems in CFD Applications
SIAM Journal on Scientific Computing
On the performance of an algebraic multigrid solver on multicore clusters
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Performance models for the Spike banded linear system solver
Scientific Programming
Characterizing the impact of soft errors on iterative methods in scientific computing
Proceedings of the international conference on Supercomputing
Modeling the performance of an algebraic multigrid cycle on HPC platforms
Proceedings of the international conference on Supercomputing
Cache injection for parallel applications
Proceedings of the 20th international symposium on High performance distributed computing
Scalable multi-coloring preconditioning for multi-core CPUs and GPUs
Euro-Par 2010 Proceedings of the 2010 conference on Parallel processing
Large scale debugging of parallel tasks with AutomaDeD
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Computer Vision and Image Understanding
Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations
SIAM Journal on Scientific Computing
Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction
SIAM Journal on Scientific Computing
Multigrid Smoothers for Ultraparallel Computing
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Parallel numerical solution of the time-harmonic maxwell equations
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Sparse matrix and solver objects for parallel finite element simulation of multi-field problems
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Combining performance aspects of irregular gauss-seidel via sparse tiling
LCPC'02 Proceedings of the 15th international conference on Languages and Compilers for Parallel Computing
Additive operator decomposition and optimization–based reconnection with applications
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Verification of variable-density flow solvers using manufactured solutions
Journal of Computational Physics
Algebraic multigrid solver on clusters of CPUs and GPUs
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Numerical solution of diffusion models in biomedical imaging on multicore processors
Journal of Biomedical Imaging - Special issue on Parallel Computation in Medical Imaging Applications
An Empirical Analysis of the Performance of Preconditioners for SPD Systems
ACM Transactions on Mathematical Software (TOMS)
Improving the efficiency of parallel FEM simulations on voxel domains
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Balancing the communications and computations in parallel FEM simulations on unstructured grids
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
A parallel two-level preconditioner for cosmic microwave background map-making
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Optimization of the multigrid-convergence rate on semi-structured meshes by local Fourier analysis
Computers & Mathematics with Applications
A Simulator for Large-Scale Parallel Computer Architectures
International Journal of Distributed Systems and Technologies
Enzo-P / Cello: scalable adaptive mesh refinement for astrophysics and cosmology
Proceedings of the Extreme Scaling Workshop
Evaluating the feasibility of using memory content similarity to improve system resilience
Proceedings of the 3rd International Workshop on Runtime and Operating Systems for Supercomputers
Computers & Mathematics with Applications
SPBC: leveraging the characteristics of MPI HPC applications for scalable checkpointing
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Architecting the finite element method pipeline for the GPU
Journal of Computational and Applied Mathematics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Design considerations for a flexible multigrid preconditioning library
Scientific Programming
Integration of emerging computer technologies for an efficient image sequences analysis
Integrated Computer-Aided Engineering
Hi-index | 0.04 |
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 [A.J. Cleary, R.D. Falgout, V.E. Henson, J.E. Jones, in: Proceedings of the Fifth International Symposium on Solving Irregularly Structured Problems in Parallel, Springer, New York, 1998] for the selection of coarse-grid points, based on modifications of certain parallel independent set algorithms and the application of heuristics 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, V.E. Henson, J.E. Jones [in: Proceedings of the Fifth International Symposium on Solving Irregularly Structured Problems in Parallel, Springer, New York, 1998] 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 conclusions regarding the efficacy of the method. Finally, we indicate the current directions of the research.