Solving hyperbolic partial differential equations using CUDA

Le résumé fourni par la source

Abstract Hyperbolic partial differential equations play a crucial role in modeling phenomena such as fluid dynamics, traffic flow, and wave interactions; due to the complexity of these equations, numerical methods are essential for obtaining solutions, particularly with the advent of parallel computing. Graphics Processing Units (GPUs), combined with NVIDIA's CUDA programming model, have enabled significant advancements in scientific computing. This work focuses on solving hyperbolic PDEs using CUDA to exploit the massive parallel processing power of GPUs. Specifically, we address Burgers' equation, the batch monodisperse sedimentation equation, and the polydisperse sedimentation model. Different numerical approaches are implemented, considering the architecture of NVIDIA GPUs and the parallel computing model. Numerical simulations are carried out to assess the efficiency and computational performance of each proposed method.

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