This thesis researches the feasibility of using algorithmic skeletons to solve computationally intensive problems on High-Performance Computing clusters with nodes that contain both multiple CPUs and multiple GPUs such as the PALMA II cluster from the University of Münster. One problem of interest to the scientific community and industry is the solution of Partial Differential Equations which this master thesis will use as a benchmark to compare the performance of a solution created using a new implementation of the mapStencil algorithmic skeleton, and another solution written entirely on its own. The comparison will provide insight to decide the value of the loss of flexibility and the gain in ease of development in terms of code performance.