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This paper presents theoretical results on instability processes in nanoscale tunneling structures that were obtained from a computationally improved physics-based simulator. The results were obtained from a numerical implementation of the Wigner-Poisson electron transport model upon a parallel- computing platform. These investigations considered various forms of multi- barrier resonant tunneling structures (RTSs) and they were used to test the robustness of the new modeling code. This improved modeling tool is shown to be fast and efficient with the potential to facilitate complete and rigorous studies of this time-dependent phenomenon. This is important because it will allow for the study of RTSs embedded in realistic circuit configurations. Hence, this advanced simulation tool will allow for the detailed study of RTS devices coupled to circuits where numerical simulations in time and iterative numerical optimization over the circuit parameters are required. Therefore, this work will enable the future study of RTS-based circuits operating at very high frequencies.