Since the recent advance in microprocessor design, the optimization of computing software becomes more and more technical. One of the difficulties is to transform sequential algorithms into parallel ones. A possible solution is the task-based design. In this approach, it is possible to describe the parallelization possibilities of the algorithm automatically. The task-based design is also a good strategy to optimize software in an incremental way. The objective of this paper is to describe a practical experience of a task-based parallelization of a Discontinuous Galerkin method in the context of electromagnetic simulations. The task-based description is managed by the StarPU runtime. Additional acceleration is obtained by OpenCL.