A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
s-step iterative methods for symmetric linear systems
Journal of Computational and Applied Mathematics
Iterative solution methods
The grid: blueprint for a new computing infrastructure
The grid: blueprint for a new computing infrastructure
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
SETI@home: an experiment in public-resource computing
Communications of the ACM
Overview of GridRPC: A Remote Procedure Call API for Grid Computing
GRID '02 Proceedings of the Third International Workshop on Grid Computing
Middleware for the use of storage in communication
Parallel Computing - Special issue: Advanced environments for parallel and distributed computing
OmniRPC: a Grid RPC ystem for Parallel Programming in Cluster and Grid Environment
CCGRID '03 Proceedings of the 3st International Symposium on Cluster Computing and the Grid
MPICH-G2: a Grid-enabled implementation of the Message Passing Interface
Journal of Parallel and Distributed Computing - Special issue on computational grids
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Improving the GridRPC Model with Data Persistence and Redistribution
ISPDC '04 Proceedings of the Third International Symposium on Parallel and Distributed Computing/Third International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks
Minimizing development and maintenance costs in supporting persistently optimized BLAS
Software—Practice & Experience - Research Articles
Cross-Site Computations on the TeraGrid
Computing in Science and Engineering
Managing data persistence in network enabled servers
Scientific Programming - Dynamic Grids and Worldwide Computing
On deflation and singular symmetric positive semi-definite matrices
Journal of Computational and Applied Mathematics
Experiments with SmartGridSolve: Achieving higher performance by improving the GridRPC model
GRID '08 Proceedings of the 2008 9th IEEE/ACM International Conference on Grid Computing
Meta-computations on the CLUSTERIX grid
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
SmartNetSolve: high-level programming system for high performance grid computing
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
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Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify the various bottlenecks induced by the middleware and the iterative algorithm. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. In addition, we improve the computation-to-communication ratio by maximising the work in the preconditioner. In addition to these algorithmic improvements, we also try to minimise the communication overhead within the communication model currently used by the GridSolve middleware. We present numerical experiments on 3D bubbly flow problems using heterogeneous computing hardware that show lower computing times and better speed-up for the Chronopoulos/Gear variant of conjugate gradients. Finally, we suggest extensions to both the iterative algorithm and the middleware for improving granularity.