Iterative numerical wear models provide valuable insight into evolving material surfaces under abrasive wear. In this paper, a holistic numerical scheme for predicting the wear of rubbing elements in tribological systems is presented. In order to capture the wear behavior of a multimaterial surface, a finite difference model is developed. The model determines pressure and height loss along a composite surface as it slides against an abrasive compliant countersurface. Using Archard's wear law, the corresponding nodal height loss is found using the appropriate material wear rate, applied pressure, and the incremental sliding distance. This process is iterated until the surface profile reaches a steady-state profile. The steady-state is characterized by the incremental height loss at each node being nearly equivalent to the previous loss in height. Several composite topologies are investigated in order to identify key trends in geometry and material properties on wear performance.