A Scalable $O(N)$ Algorithm for Large-Scale Parallel First-Principles Molecular Dynamics Simulations

Abstract

Traditional algorithms for first-principles molecular dynamics (FPMD) simulations only gain a modest capability increase from current petascale computers, due to their $O(N^3)$ complexity and their heavy use of global communications. To address this issue, we are developing a truly scalable $O(N)$ complexity FPMD algorithm, based on density functional theory (DFT), which avoids global communications. The computational model uses a general nonorthogonal orbital formulation for the DFT energy functional, which requires knowledge of selected elements of the inverse of the associated overlap matrix. We present a scalable algorithm for approximately computing selected entries of the inverse of the overlap matrix, based on an approximate inverse technique, by inverting local blocks corresponding to principal submatrices of the global overlap matrix. The new FPMD algorithm exploits sparsity and uses nearest neighbor communication to provide a computational scheme capable of extreme scalability. Accuracy is contr...