A scalable sparse eigensolver for petascale applications

Exploiting locality of chemical interactions and therefore sparsity is necessary to push the limits of quantum simulations beyond petascale. However, sparse numerical algorithms are known to have poor strong scaling. Here, we show that shift-and-invert parallel spectral transformations (SIPs) method can scale up to two-hundred thousand cores for density functional based tight-binding (DFTB), or semi-empirical molecular orbital (SEMO) applications. We demonstrated the robustness and scalability of the SIPs method on various kinds of systems including metallic carbon nanotubes, diamond crystals and water clusters. We analyzed how sparsity patterns and eigenvalue spectrums of these different type of applications affect the computational performance of the SIPs. The SIPs method enables us to perform simulations with more than five hundred thousands of basis functions utilizing more than hundreds of thousands of cores. SIPs has a better scaling for memory and computational time in contrast to dense eigensolvers, and it does not require fast interconnects.