Grid computing technology addresses the growing need for computing resources in simulation-based engineering and science (SBES). However, optimal performance of grid computing technology requires 'virtually tightly coupled' computing resources. This, though, may not be economically available in many research societies. In this work, we propose a new approach to improve performance of a typical parallel application for SBES on a 'virtually not tightly coupled' grid computing environment. To this end, we have proposed, implemented, and investigated the performance of a new grid programming technique based on the Global Arrays toolkit and multi-level topology-aware approach. We have found that performance of the evaluating application implemented with this new technique outperforms both MPICH-G2 and native Global Arrays implementations, but is still comparable to that of the application implemented with OpenMP, the native Symmetric-Multi Processors programming.