Parallel Krylov Subspace Methods are commonly used for solving large-scale sparse linear systems. Facing the development of extreme scale platforms, the minimization of synchronous global communication becomes critical to obtain good efficiency and scalability. This paper highlights a recent development of a hybrid (unite and conquer) method, which combines three computation algorithms together with asynchronous communication to accelerate the resolution of non-Hermitian linear systems and to improve its fault tolerance and reusability. Experimentation shows that our method has an up to 5× speedup and better scalability than the conventional methods for the resolution on hierarchical clusters with hundreds of nodes.
In this paper we propose a new approach for calculating some eigenpairs of large sparse non-Hermitian matrices. This method, called Multiple Explicitly Restarted Arnoldi (MERAM), is particularly well suited for environments that combine different parallel programming paradigms. This technique is based on a multiple use of the Explicitly Restarted Arnoldi method (ERAM) and improves its convergence.This technique is implemented and tested on a distributed environment consisting of two interconnected parallel machines. The MERAM technique is compared with ERAM, and one can notice that the convergence is improved. In some cases, more than a twofold improvement can be seen in MERAM results.We also implemented MERAM on a cluster of workstations. According to our experiments, MERAM converges better than the Explicitly Restarted Block Arnoldi method and, for some matrices, more quickly than the PARPACK package, which implements the Implicitly Restarted Arnoldi method.
Peer to peer and grid systems provide attractive middlewares to solve large numerical problems. The development, deployment and execution of applications using those middlewares suffer from the lack of well-adapted advanced tools. There is not any available solution to use the same application on two distinct middlewares. Our article presents the YML Framework which provides supporting tools to design and execute portable parallel applications over large scale peer to peer and grid middlewares. The YML Framework defines a new parallel programming language called YvetteML which is composed of a graph language and a component model. We evaluate the performance of our framework with a simple numerical application using XtremWeb as a middleware.
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