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This article describes the implementation of an all-in-one numericalprocedure within the runtime StarPU. In order to limit the complexity of themethod, for the sake of clarity of the presentation of the non-classicaltask-driven programming environnement, we have limited the numerics to firstorder in space and time. Results show that the task distribution is efficientif the tasks are numerous and individually large enough so that the task heapcan be saturated by tasks which computational time covers the task managementoverhead. Next, we also see that even though they are mostly faster on graphiccards, not all the tasks are suitable for GPUs, which brings forward theimportance of the task scheduler. Finally, we look at a more realistic systemof conservation laws with an expensive source term, what allows us to concludeand open on future works involving higher local arithmetic intensity, byincreasing the order of the numerical method or by enriching the model(increased number of parameters and therefore equations).

A task-driven implementation of a simple numerical solver for hyperbolic conservation laws