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TL;DR: This article explores the implementation and performance of the PM (Particle Mesh) and P3M (Particle-Particle Particle-Mesh) algorithms on GPUs, highlighting their efficiency in astrophysical simulations. Using GLSL language and Vulkan API, the algorithms are adapted for compatibility with a wide range of GPUs, including mid-range gaming graphics cards and integrated GPUs like Apple's M1 and M2.

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