The discrete element method (DEM) is particularly well adapted to simulate the mesoscale interactions of heterogeneous systems, such as concrete, to understand the nature of macro behavior. The traditional DEM-based approach uses an explicit time integration algorithm to track the contact interactions and simulate an assembly comprising a large number of particles to better understand the influence of mesostructure on macro behavior. This results in a heavy computation burden, since the computation time required is enormous, since very small-time increments (of the order \(10^{ - 8} {\text{s}}\) or less) have to be used in order to meet the stability requirements. The Adaptive Dynamic Relaxation (ADR) method is a means to address this issue. The steady-state solution can be found with the ADR method through dynamic transient analysis. It relies on introducing artificial inertia and damping forces into the static equation, transforming it into a dynamic system. The right choice of ADR artificial components leads to faster rates of convergence and a sharp reduction in computation costs. Modifications to the standard ADR algorithm to improve the convergence rate are described. The modified ADR algorithm significantly reduces computation costs for a class of problems.