A Robust and Efficient Implementation of LOBPCG

doi:10.1137/17M1129830

Title: A Robust and Efficient Implementation of LOBPCG

Full Record
Other Related Research

Abstract

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. In this paper we propose an improved basis selection strategy based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence criterion which is backward stable to enhance the robustness. Here, we also suggest several algorithmic optimizations that improve performance of practical LOBPCG implementations. Numerical examples confirm that our approach consistently and significantly outperforms previous competing approaches in both stability and speed.

Authors:

Duersch, Jed A. ^[1];

^[2]; Yang, Chao ^[2]; Gu, Ming ^[3]

Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.

Publication Date:: 2018-10-04

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1525270

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing

Additional Journal Information:: Journal Volume: 40; Journal Issue: 5; Journal ID: ISSN 1064-8275

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: symmetric eigenvalue problem; LOBPCG; numerical stability

Citation Formats


                    Duersch, Jed A., Shao, Meiyue, Yang, Chao, and Gu, Ming. A Robust and Efficient Implementation of LOBPCG.  United States: N. p., 2018. 
        Web.  doi:10.1137/17M1129830.

Copy to clipboard


                    Duersch, Jed A., Shao, Meiyue, Yang, Chao, & Gu, Ming. A Robust and Efficient Implementation of LOBPCG.  United States.  doi:10.1137/17M1129830.

Copy to clipboard


                    Duersch, Jed A., Shao, Meiyue, Yang, Chao, and Gu, Ming. Thu .  
        "A Robust and Efficient Implementation of LOBPCG".  United States.  doi:10.1137/17M1129830.  https://www.osti.gov/servlets/purl/1525270.

Copy to clipboard


                    
@article{osti_1525270,

  title        = {A Robust and Efficient Implementation of LOBPCG},

  author       = {Duersch, Jed A. and Shao, Meiyue and Yang, Chao and Gu, Ming},

  abstractNote = {Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. In this paper we propose an improved basis selection strategy based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence criterion which is backward stable to enhance the robustness. Here, we also suggest several algorithmic optimizations that improve performance of practical LOBPCG implementations. Numerical examples confirm that our approach consistently and significantly outperforms previous competing approaches in both stability and speed.},

  doi          = {10.1137/17M1129830},

  journal      = {SIAM Journal on Scientific Computing},

  number       = 5,

  volume       = 40,

  place        = {United States},

  year         = {2018},

  month        = {10}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: 10.1137/17M1129830

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]

Journal Article Pandare, Aditya K. ; Luo, Hong - Journal of Computational Physics

A robust and efficient density-based finite volume method is developed for solving the six-equation single pressure system of two-phase flows at all speeds on hybrid unstructured grids. Unlike conventional approaches where an expensive exact Riemann solver is normally required for computing numerical fluxes at the two-phase interfaces in addition to AUSM-type fluxes for single-phase interfaces in order to maintain stability and robustness in cases involving interactions of strong pressure and void-fraction discontinuities, a volume-fraction coupling term for the AUSM ⁺-up fluxes is introduced in this work to impart the required robustness without the need of the exact Riemann solver. Themore »« less
Cited by 2
DOI: 10.1016/j.jcp.2018.05.018

Full Text Available
Exploring Valleys without Climbing Every Peak: More Efficient and Forgiving Metabasin Metadynamics via Robust On-the-Fly Bias Domain Restriction

Journal Article Dama, James F. ; Hocky, Glen M. ; Sun, Rui ; ... - Journal of Chemical Theory and Computation

Metadynamics is an enhanced sampling method designed to flatten free energy surfaces uniformly. However, the highest-energy regions are often irrelevant to study and dangerous to explore because systems often respond irreversibly in unforeseen ways in response to driving forces in these regions, spoiling the sampling. Introducing an on-the-fly domain restriction allows metadynamics to flatten only up to a specified energy level and no further, improving efficiency and safety while decreasing the pressure on practitioners to design collective variables that are robust to otherwise irrelevant high energy driving. Here this paper describes a new method that achieves this using sequential on-the-flymore »« less
Cited by 13
DOI: 10.1021/acs.jctc.5b00907

Full Text Available
A robust and efficient method for the extraction of plant extracellular surface lipids as applied to the analysis of silks and seedling leaves of maize

Journal Article Loneman, Derek M. ; Peddicord, Layton ; Al-Rashid, Amani ; ... - PLoS ONE

Aerial plant organs possess a diverse array of extracellular surface lipids, including both non-polar and amphipathic constituents that collectively provide a primary line of defense against environmental stressors. Extracellular surface lipids on the stigmatic silks of maize are composed primarily of saturated and unsaturated linear hydrocarbons, as well as fatty acids, and aldehydes. To efficiently extract lipids of differing polarities from maize silks, five solvent systems (hexanes; hexanes:diethyl ether (95:5); hexanes:diethyl ether (90:10); chloroform:hexanes (1:1) and chloroform) were tested by immersing fresh silks in solvent for different extraction times. Surface lipid recovery and the relative composition of individual constituents weremore »« less
DOI: 10.1371/journal.pone.0180850

Full Text Available
Exploring Valleys without Climbing Every Peak: More Efficient and Forgiving Metabasin Metadynamics via Robust On-the-Fly Bias Domain Restriction

Journal Article Dama, James F. ; Hocky, Glen M. ; Sun, Rui ; ... - Journal of Chemical Theory and Computation

Metadynamics is an enhanced sampling method designed to flatten free energy surfaces uniformly. However, the highest-energy regions are often irrelevant to study and dangerous to explore because systems often respond irreversibly in unforeseen ways in response to driving forces in these regions, spoiling the sampling. Introducing an on-the-fly domain restriction allows metadynamics to flatten only up to a specified energy level and no further, improving efficiency and safety while decreasing the pressure on practitioners to design collective variables that are robust to otherwise irrelevant high energy driving. Here this paper describes a new method that achieves this using sequential on-the-flymore »« less
Cited by 13
DOI: 10.1021/acs.jctc.5b00907

Full Text Available
Molecular ligand modulation of palladium nanocatalysts for highly efficient and robust heterogeneous oxidation of cyclohexenone to phenol

Journal Article Xue, Teng ; Lin, Zhaoyang ; Chiu, Chin-Yi ; ... - Science Advances

Metallic nanoparticles are emerging as an exciting class of heterogeneous catalysts with the potential advantages of exceptional activity, stability, recyclability, and easier separation than homogeneous catalysts. The traditional colloid nanoparticle syntheses usually involve strong surface binding ligands that could passivate the surface active sites and result in poor catalytic activity. The subsequent removal of surface ligands could reactivate the surface but often leads to metal ion leaching and/or severe Ostwald ripening with diminished catalytic activity or poor stability. Molecular ligand engineering represents a powerful strategy for the design of homogeneous molecular catalysts but is insufficiently explored for nanoparticle catalysts tomore »« less
Cited by 3
DOI: 10.1126/sciadv.1600615

Full Text Available

Similar Records