This study presents an accelerated implementation of a two-dimensional moving mesh point correspondence algorithm using a GPU for tracking mobile tumor boundaries during radiation therapy. Normal CPU implementation of this algorithm is computationally intensive and time-consuming which limits its clinical utility, hence the need for a faster GPU implementation. One of the computationally intensive parts of the registration algorithm involves numerically solving a partial differential equation. In this paper we demonstrate that the computational performance of the algorithms can be improved by utilizing a shared memory implementation on the GPU. Evaluations in comparison to 600 manually drawn contours showed that the proposed GPU-based tracking of the tumor boundaries yielded similar level of accuracy as the CPU based approach with improved computational efficiency.