Kohn-Sham Density Functional Theory (DFT) is the most widely used electronic structure calculation method in quantum chemistry, solid state physics, and materials science. Since DFT calculations use about 15% of the total resources available in high-performance scientific computing centers, finding more efficient numerical methods for the Kohn-Sham model is of major interest. This requires a better understanding of the mathematical and numerical properties of the Kohn-Sham model. I will present some recent results in this direction, as well as some challenges.
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