A multi-grained distributed implementation of the parallel Block Conjugate Gradient algorithm

The Block Conjugate Gradient algorithm (Block‐CG) was developed to solve sparse linear systems of equations that have multiple right‐hand sides. We have adapted it for use in heterogeneous, geographically distributed, parallel architectures. Once the main operations of the Block‐CG (Tasks) have been collected into smaller groups (subjobs), each subjob is matched by the middleware MJMS (MPI Jobs Management System) with a suitable resource selected among those which are available. Moreover, within each subjob, concurrency is introduced at two different levels and with two different granularities: the coarse‐grained parallelism to perform independent tasks and the fine‐grained parallelism within the execution of a task. We refer to this algorithm as to multi‐grained distributed implementation of the parallel Block‐CG. We compare the performance of a parallel implementation with the one of the distributed implementation running on a variety of Grid computing environments. The middleware MJMS—developed by some of the authors and built on top of Globus Toolkit and Condor‐G—was used for co‐allocation, synchronization, scheduling and resource selection. Copyright © 2010 John Wiley & Sons, Ltd.