In this paper, we discuss the ability to numerically minimize the grand potential of hard disks in two-dimensional and of hard spheres in three-dimensional space within the framework of classical density functional and fundamental measure theory on modern graphics cards. Our main finding is that a massively parallel minimization leads to an enormous performance gain in comparison to standard sequential minimization schemes. Furthermore, the results indicate that in complex multi-dimensional situations, a heavy parallel minimization of the grand potential seems to be mandatory in order to reach a reasonable balance between accuracy and computational cost.
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