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The main contribution of this work is the development of a distributed memory architecture for the Distributed Geometric Machine Environment (D-GM) by using a distributed shared memory software implementation (DSM) named ShareD-GM. This work considers the use of the Terracotta system, based on its characteristics which meet all the requirements to implement the distributed memory of the D-GM environment. The development of the ShareDGM contributes to a better dynamical execution with major functionality. The evaluation of this integration was made by the Jacobi algorithm case study. The execution of such method in the proposed implementation and in the previous implementation of the D-GM environment allowed for comparison between the runtimes and speedup, attesting an effective performance improvement.