### Large-scale electronic structure calculations

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** Kristopher Andersen,
University of California, Davis **

First-principles electronic structure calculations determine material properties using the fundamental equations of quantum mechanics. The computational bottleneck of these calculations is typically the self-consistent solution of Schrödinger (or Kohn-Sham) equations, which in turn require the repeated solution of large eigenvalue problems of dimension *n* = 10^{5}-10^{6} for the lowest *m* = 10^{2}-10^{3} eigenvalues and eigenvectors. Recently, a new method to solve large eigenvalue problems has been pioneered by A. Knyazev, the locally-optimal conjugate gradient method. Variants of this method will be discussed in the context of electronic structure calculations, focusing specifically on a real-space formulation of density-functional theory using a finite-element basis set.

**Abstract Author(s):** Kristopher E. Andersen and John E. Pask