I have recently encountered this paper in which the authors have formulated Kohn-Sham equations using the finite elements package deal.II, leading to an open-source software called DFT-FE. It stated in the paper:

"DFT-FE was significantly faster than QE for all the systems considered, with speedups for smaller system sizes (2550–6034 electrons) to speedups for larger system sizes (14,322–20,470 electrons)"

Can somebody comment on the theory and resulting scaling of speed? As the package is recently developed, what are the challenges that will come on the practical side for calculating properties of materials in the future?



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