Abstract Submitted for the MAR16 Meeting of The American Physical Society Spectral Gauss quadrature method with subspace interpolation for Kohn-Sham Density functional theory

Submitted for the MAR16 Meeting of The American Physical Society Spectral Gauss quadrature method with subspace interpolation for Kohn-Sham Density functional theory XIN WANG, US Army Rsch Lab Aberdeen — Algorithms with linear-scaling (O(N )) computational complexity for Kohn-Sham density functional theory (K-S DFT) is crucial for studying molecular systems beyond thousands of atoms. Of the O(N ) methods that use a polynomialbased approximation of the density matrix, the linear-scaling spectral Gauss quadrature (LSSGQ) method (Suryanarayana et al., JMPS, 2013) has been shown to exhibit the fastest convergence. The LSSGQ method requires a Lanczos procedure at every node in a real-space mesh, leading to a large computational pre-factor. We propose a new interpolation scheme specific to the LSSGQ method that lift the need to perform a Lanczos procedure at every node in the real-mesh. This interpolation will be referred to as subspace interpolation. The key idea behind subspace interpolation is that there is a large overlap in the Krylov-subspaces produced by the Lanczos procedures of nodes that are close in real-space. The subspace interpolation scheme takes advantage of the block-Lanczos procedure to group the Krylov-subspaces from a few representative nodes to approximate the density matrix over a large collection of nodes. Subspace interpolation outperforms cubic-spline interpolation by several orders of magnitude. Xin Wang US Army Rsch Lab Aberdeen Date submitted: 22 Dec 2015 Electronic form version 1.4