Ion-beam processing of materials is widely supported by atomistic simulations by means of molecular dynamics. Although the approach has given several valuable insights, it has a limited operational window in both time and length scales. In particular, for high-fluence ion irradiation with multiple consecutive cascades, the direct molecular dynamics method becomes prohibitively time consuming.In this work, we propose a speed-up algorithm for molecular-dynamics simulations of multiple consecutive collision cascades employing an adaptive moving environment model. In the model, the computational power is primarily focused on calculating the atomic movement in the propagating cascade regions, while thermally equilibrated regions outside the cascades are excluded. Up to a five-fold efficiency increase was seen with the adaptive moving environment compared to classical molecular dynamics, without any significant statistical difference in the results of multiple individual ion-cascade simulations in a heterostructure of alternating Si and SiO2 layers. Simulations of temperature-driven dynamic annealing during high-fluence ion irradiation of Si nanopillars at elevated temperatures using the adaptive moving environment showed similar trends as experiments with respect to temperature dependence. The model is included in the atomistic simulator toolkit, COSIRMA (COmputer Simulator for IRradiation of MAterials), and can easily be enabled through the user-friendly graphical interface.