A generalization of the numerical schwarz algorithm
Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, VI
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Multisplitting of a symmetric positive definite matrix
SIAM Journal on Matrix Analysis and Applications
Analysis and comparison of two general sparse solvers for distributed memory computers
ACM Transactions on Mathematical Software (TOMS)
Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
ACM Transactions on Mathematical Software (TOMS)
A new scheduling algorithm for parallel sparse LU factorization with static pivoting
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Asynchronism for Iterative Algorithms in a Global Computing Environment
HPCS '02 Proceedings of the 16th Annual International Symposium on High Performance Computing Systems and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Decentralized Convergence Detection Algorithm for Asynchronous Parallel Iterative Algorithms
IEEE Transactions on Parallel and Distributed Systems
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
GREMLINS: a large sparse linear solver for grid environment
Parallel Computing
APPT'07 Proceedings of the 7th international conference on Advanced parallel processing technologies
The Journal of Supercomputing
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The goal of this paper is to introduce a new approach to the building of efficient distributed linear system solvers. The starting point of the results of this paper lies in the fact that the parallelization of direct algorithms requires frequent synchronizations in order to obtain the solution for a linear problem. In a grid computing environment, communication times are significant and the bandwidth is variable, therefore frequent synchronizations slow down performances. Thus it is desirable to reduce the number of synchronizations in a parallel direct algorithm. Inspired from multisplitting techniques, the method we present consists in solving several linear problems obtained by splitting the original one. Each linear system is solved independently on a cluster by using the direct method. This paper uses the theoretical results of [Asynchronous multisplitting methods for nonlinear fixed point problems] in order to build coarse grained algorithms designed for solving linear systems in the grid computing context.