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

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fattebert, Jean-Luc Osei-Kuffuor, Daniel
Copyright Year	2014
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 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, with a wall-clock time of $O(1)$ minute per molecular dynamics time step.
Starting Page	C353
Ending Page	C375
Page Count	23
File Format	PDF
ISSN	10648275
DOI	10.1137/140956476
e-ISSN	10957197
Issue Number	4
Volume Number	36
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-08-21
Access Restriction	Subscribed
Subject Keyword	large scale molecular dynamics gram matrix inverse density functional theory Approximation algorithms linear scaling algorithms parallel approximate inverse Sparse matrices Parallel algorithms Distributed algorithms Applications to physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in