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

Traditional algorithms for first-principles molecular dynamics (FPMD) simulations only gain a modest capability increase from current petascale computers, due to their O(N3) 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 controlled by the mesh spacing of the finite difference discretization, the size of the localization regions in which the electronic orbitals are confined, and a cutoff beyond which the entries of the overlap matrix can be omitted when computing selected entries of its inverse. We demonstrate the algorithm's excellent parallel scaling for up to O(100K) atoms on O(100K) processors, withmore » a wall-clock time of O(1) minute per molecular dynamics time step.« less
Authors:
 [1] ;  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
1165754
DOE Contract Number:
DE-AC52-07NA27344
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 36; Journal Issue: 4
Research Org:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE LINEAR SCALING ALGORITHMS; DENSITY FUNCTIONAL THEORY; GRAM MATRIX INVERSE; LARGE SCALE MOLECULAR DYNAMICS; PARALLEL APPROXIMATE INVERSE