<p>Convexification-based approaches to damage mechanics emerged recently as powerful alternatives to non-local or gradient-augmented damage models. Convexifying the incremental potentials leads to a damage-transport equation at material-point level, and a simple modification based on entropic regularization was recently shown to give rise to a continuum damage model which shows softening yet whose incremental potentials are strongly convex, ensuring well-posedness of the boundary-value problem and efficiency of computational resolution. These salient properties come at a price: The damage-transport equation, an advection-type equation, must be solved at each material point. The latter involves a discretization of the attainable damage states and seeks a large number of transition coefficients. The work at hand introduces a novel reformulation of the damage-transport equation as a one-dimensional root-finding problem. Once this problem is solved, the transition coefficients may be obtained in post-processing. We discuss the monotonicity and uniqueness properties of the one-dimensional function whose root is sought, provide a simple yet robust computational strategy for its resolution and study the efficiency of the approach in dedicated computational experiments.</p>