  We develop a Continuous Hugoniot Method for the efficient simulation of shock
wave fronts with molecular dynamics. This approach achieves a significantly
improved efficiency in the generation of a dense sampling of steady-state shock
front states, and allows for the study of shocks as a function of a continuous
shock strength parameter, $v_p$. This is, to our knowledge, the first attempt
to map out the Hugoniot in a continuous fashion.
  We first apply this method to shocks in single-crystal Lennard-Jonesium along
the <100> direction. Excellent agreement is found with both the published
Lennard-Jones Hugoniot and results of conventional simulation methods.
  We next present a continuous numerical Hugoniot for shocks in tin which
agrees to within 6% with experimental data. We study the strong shock to
elastic-plastic shock transition in tin and find that it is a continuous
transition consistent with a transcritical bifurcation.
