The stochastic density functional theory (sDFT) has exhibited several advantages over the traditional Kohn-Sham DFT method and has become an attractive approach in electronic structure calculations. The sDFT method avoids expensive matrix diagonalization by introducing a set of random orbitals and approximating the density matrix via Chebyshev expansion of a matrix function. In this work, we study the sDFT with the planewave discretization, and discuss various variance reduction algorithms in the framework of multi-level Monte Carlo (MLMC) methods. In particular, we show that the evaluation of the density matrix in sDFT can be decomposed into many levels by increasing the planewave energy cutoffs and the Chebyshev polynomial orders, which can lead to a significant variance reduction. We demonstrate the efficiency of the combination of sDFT with MLMC methods by providing rigorous analysis on the statistical errors, and presenting numerical experiments on some material systems.

Refreshments will be served preceding the talk, starting at 2:45 pm.