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Title: Pole EXpansion and Selected Inversion (PEXSI)

Abstract

The Pole EXpansion and Selected Inversion method (PEXSI) is a fast method for evaluating certain selected elements of a matrix function. PEXSI is highly scalable on distributed memory parallel machines. For sparse matrices, the PEXSI method can be more efficient than the widely used diagonalization method for evaluating matrix functions, especially when a relatively large number of eigenpairs are needed to be computed in the diagonalization methond

Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory
Sponsoring Org.:
USDepartment of Energy
Contributing Org.:
Lin Lin, Mathias Jacquelin, Chao Yang
OSTI Identifier:
1231762
Report Number(s):
PEXSI; 003003MLTPL00
2014-072
DOE Contract Number:
AC02-05CH11231
Resource Type:
Software
Software Revision:
00
Software Package Number:
003003
Software Package Contents:
Software package available from Lawrence Berkeley National Laboratory at the following URL: http://pexsi.github.io/pexsi/
Software CPU:
MLTPL
Open Source:
No
Source Code Available:
Yes
Related Software:
SuperLU_DIST, ParMETIS/PT-SCOTCH
Country of Publication:
United States

Citation Formats

. Pole EXpansion and Selected Inversion (PEXSI). Computer software. Vers. 00. USDepartment of Energy. 1 Mar. 2014. Web.
. (2014, March 1). Pole EXpansion and Selected Inversion (PEXSI) (Version 00) [Computer software].
. Pole EXpansion and Selected Inversion (PEXSI). Computer software. Version 00. March 1, 2014.
@misc{osti_1231762,
title = {Pole EXpansion and Selected Inversion (PEXSI), Version 00},
author = {},
abstractNote = {The Pole EXpansion and Selected Inversion method (PEXSI) is a fast method for evaluating certain selected elements of a matrix function. PEXSI is highly scalable on distributed memory parallel machines. For sparse matrices, the PEXSI method can be more efficient than the widely used diagonalization method for evaluating matrix functions, especially when a relatively large number of eigenpairs are needed to be computed in the diagonalization methond},
doi = {},
year = {Sat Mar 01 00:00:00 EST 2014},
month = {Sat Mar 01 00:00:00 EST 2014},
note =
}

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  • We describe how to apply the recently developed pole expansion plus selected inversion (PEpSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating charge density, total energy, Helmholtz free energy and atomic forces without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEpSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing themore » timing of PEpSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEpSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEpSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes on a single processor. We also show that the use of PEpSI does not lead to loss of accuracy required in a practical DFT calculation.« less
  • This report presents the results of a customer telephone survey of the users of two software programs provided by the U. S. Department of Energy Federal Energy Management Program (FEMP) during calendar years 1995 and 1996. The primary purpose for the survey is to provide the Team Leader to FEMP Technical Assistance and members of the team with detailed customer feedback pertaining to how well selected FEMP software programs are being used and to identify areas for improvement. The information presented enables managers to see both the strengths of their software programs and software components that can be improved. Themore » survey was conducted during the fall of 1997 in conjunction with a FEMP workshop attendee survey. The results of the workshop survey are presented is a sister document entitled, ''An Evaluation of the Federal Energy Management Program's Technical Assistance Workshops.« less

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