Hardware accelerators (such as the Cell Broadband Engine) have recently received a significant amount of attention from the computational science community because they can provide significant gains in the overall performance of many numerical simulations at a low cost. However, such accelerators usually employ a rather unfamiliar and specialized programming model that often requires advanced knowledge of their hardware design. In this article, we demonstrate an alternate and simpler approach toward managing the main complexities in the programming of the cell processor, called software caching. We apply this technique to a numerical relativity (NR) application: a time-domain, finite-difference Kerr black hole perturbation evolver, and present the performance results. We obtain gains in the overall performance of generic simulations that are close to the theoretical maximum that can be obtained through our parallelization approach.