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We describe a Continuous Hugoniot Method for the efficient simulation of shock wave fronts. This approach achieves significantly improved efficiency when the generation of a tightly spaced collection of individual steady-state shock front states is desired, and allows for the study of shocks as a function of a continuous shock strength parameter, vp. This is, to our knowledge, the first attempt to map the Hugoniot continuously. We apply the method to shock waves in Lennard-Jonesium along the <100> direction. We obtain very good agreement with prior simulations, as well as our own benchmark comparison runs. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]