Nanostructures have been proposed for many applications including solar cells for renewable
energy, new materials for batteries, and biomedical imaging. To fully explore these ideas
however, requires ab initio materials simulations. Today, these codes are usually based on Density Functional Theory (DFT) that are used for computing the ground state energy and the
corresponding single particle wave functions associated with a many-electron atomistic system.
At the heart of these codes, one typically finds a Self Consistent Field (SCF) iteration. In this
talk, we propose an optimization procedure that minimizes the Kohn-Sham total energy directly.
We point out the similarities between our new approach and SCF and show how the SCF iteration
can fail. However, by introducing a trust region technique we can improve the robustness of both
methods. Numerical examples demonstrate the combination of these approaches on several model
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