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

## TL;DR

This paper presents a task-driven implementation of a simple first-order numerical solver for hyperbolic conservation laws within the StarPU runtime, analyzing efficiency, GPU suitability, and potential for higher-order methods.

## Contribution

It introduces a task-based approach for hyperbolic conservation laws and evaluates its performance and scalability on heterogeneous computing systems.

## Key findings

- Task distribution is efficient with numerous large tasks.
- GPU acceleration benefits are limited to suitable tasks.
- Higher local arithmetic intensity can be achieved with more complex models.

## Abstract

This article describes the implementation of an all-in-one numerical procedure within the runtime StarPU. In order to limit the complexity of the method, for the sake of clarity of the presentation of the non-classical task-driven programming environnement, we have limited the numerics to first order in space and time. Results show that the task distribution is efficient if the tasks are numerous and individually large enough so that the task heap can be saturated by tasks which computational time covers the task management overhead. Next, we also see that even though they are mostly faster on graphic cards, not all the tasks are suitable for GPUs, which brings forward the importance of the task scheduler. Finally, we look at a more realistic system of conservation laws with an expensive source term, what allows us to conclude and open on future works involving higher local arithmetic intensity, by increasing the order of the numerical method or by enriching the model (increased number of parameters and therefore equations).