Emanuel Rubensson: Efficient methods for large electronic structure calculations

With the steady increase of computational processing power, atomistic simulations based on quantum mechanical electronic structure calculations have become a powerful tool for studies of many problems in materials science, chemistry, and biology. Nevertheless, applications are limited to rather small systems since the computational cost of electronic structure calculations grows rapidly with system size. The expensive, cubically scaling, O(N^3), solution of the quantum mechanical eigenvalue problem has been particularly limiting. In this talk we will see how this bottleneck can be avoided with a computational effort that increases only linearly with system size. This is accomplished by the use of fast polynomial expansions combined with efficient libraries for sparse matrix algebra.