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The global arrays toolkit is a library that allows programmers to write parallel programs that use large arrays distributed across processing nodes through the aggregate remote memory copy interface (ARMCI). In this study, we have further our investigation on the performance of a parallel application implemented with the global arrays toolkit on homogeneous grid computing environments. Two types of the homogeneous grid computing environments have been examined in this study. In order to fully take advantage of the global arrays toolkit, the topology-aware and multi-level parallelism have been also implemented in the evaluating application. We have found that the current implementation of the evaluating application outperform both MPICH-G2 and a typical global arrays implementations in all studied cases.