Efficient Multigrid algorithms for locally constrained parallel systems
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
Communications of the ACM
Multigrid methods on parallel computers—a survey of recent developments
IMPACT of Computing in Science and Engineering
Scientific computing: an introduction with parallel computing
Scientific computing: an introduction with parallel computing
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Performance properties of large scale parallel systems
Journal of Parallel and Distributed Computing - Special issue on performance of supercomputers
Analyzing scalability of parallel algorithms and architectures
Journal of Parallel and Distributed Computing - Special issue on scalability of parallel algorithms and architectures
Scalability aspects of parallel multigrid
Future Generation Computer Systems - Special issue: BECAUSE workshop part I
Performance and Scalability of Preconditioned Conjugate Gradient Methods on Parallel Computers
IEEE Transactions on Parallel and Distributed Systems
Early prediction of MPP performance: the SP2, T3D, and Paragon experiences
Parallel Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Advanced Computer Architecture: Parallelism,Scalability,Programmability
Advanced Computer Architecture: Parallelism,Scalability,Programmability
Isoefficiency: Measuring the Scalability of Parallel Algorithms and Architectures
IEEE Parallel & Distributed Technology: Systems & Technology
Scalability of Parallel Algorithm-Machine Combinations
IEEE Transactions on Parallel and Distributed Systems
A3: a simple and asymptotically accurate model for parallel computation
FRONTIERS '96 Proceedings of the 6th Symposium on the Frontiers of Massively Parallel Computation
Architecture, algorithms and applications for future generation supercomputers
FRONTIERS '96 Proceedings of the 6th Symposium on the Frontiers of Massively Parallel Computation
THE RELATION OF SCALABILITY AND EXECUTION TIME
THE RELATION OF SCALABILITY AND EXECUTION TIME
Data Locality Exploitation in the Decomposition of Regular Domain Problems
IEEE Transactions on Parallel and Distributed Systems
A Parallel Robust Multigrid Algorithm Based on Semi-Coarsening
Proceedings of the 6th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Parallelization of a method for the solution of the inverse additive singular value problem
MATH'05 Proceedings of the 8th WSEAS International Conference on Applied Mathematics
Uintah: a scalable framework for hazard analysis
Proceedings of the 2010 TeraGrid Conference
A robust multigrid solver on parallel computers
EURO-PDP'00 Proceedings of the 8th Euromicro conference on Parallel and distributed processing
Scalability analysis of parallel systems with multiple components of work
EURO-PDP'00 Proceedings of the 8th Euromicro conference on Parallel and distributed processing
Integrating teaching and research in HPC: experiences and opportunities
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
DAG-Based software frameworks for PDEs
Euro-Par'11 Proceedings of the 2011 international conference on Parallel Processing
High-Performance Computing for Data Analytics
DS-RT '12 Proceedings of the 2012 IEEE/ACM 16th International Symposium on Distributed Simulation and Real Time Applications
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The large number of processing elements in current parallel systems necessitates the development of more comprehensive and realistic tools for the scalability analysis of algorithms on those architectures. This paper presents a simple analytical tool with which to study the scalability of parallel algorithm-architecture combinations. Our practical method studies separately execution time, efficiency, and memory usage in the accuracy-critical scaling model, where the problem size驴input data set size驴increases with the number of processors, which is the relevant one in many situations. The paper defines quantitative and qualitative measurements of the scalability and derives important relationships between execution time and efficiency. For example, results show that the best way to scale the system (to deteriorate as little as possible the properties of the system) is by maintaining constant execution time. These analytical results are verified with one candidate application for massive parallel computers: the full multigrid method. We study the scalability of a general d-dimensional full multigrid method on an r-dimensional mesh of processors. The analytical expressions are verified through experimental results obtained by implementing the full multigrid method on a Transputer-based machine and on the CRAY T3D.