Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

Shao, Meiyue; Aktulga, H.  Metin; Yang, Chao; Ng, Esmond G.; Maris, Pieter; Vary, James P.

doi:10.1016/j.cpc.2017.09.004

Title: Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

Abstract

In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. The use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

Authors:

^[1]; Aktulga, H. Metin ^[2]; Yang, Chao ^[1]; Ng, Esmond G. ^[1]; Maris, Pieter ^[3]; Vary, James P. ^[3]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
Michigan State Univ., East Lansing, MI (United States). Dept. of Computer Science and Engineering
Iowa State Univ., Ames, IA (United States). Dept. of Physics and Astronomy

Publication Date:: Thu Sep 14 00:00:00 EDT 2017

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

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP); Michigan State Univ. (United States)

OSTI Identifier:: 1439235

Alternate Identifier(s):: OSTI ID: 1550011

Grant/Contract Number:: AC02-05CH11231; SC0008485; FG02-87ER40371; GE100082; DESC0008485

Resource Type:: Accepted Manuscript

Journal Name:: Computer Physics Communications

Additional Journal Information:: Journal Volume: 222; Journal ID: ISSN 0010-4655

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; nuclear configuration interaction; symmetric eigenvalue problem; LOBPCG; preconditioning

Citation Formats


                    Shao, Meiyue, Aktulga, H.  Metin, Yang, Chao, Ng, Esmond G., Maris, Pieter, and Vary, James P. Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver.  United States: N. p., 2017. 
Web.  doi:10.1016/j.cpc.2017.09.004.

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                    Shao, Meiyue, Aktulga, H.  Metin, Yang, Chao, Ng, Esmond G., Maris, Pieter, & Vary, James P. Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver.  United States.  https://doi.org/10.1016/j.cpc.2017.09.004

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                    Shao, Meiyue, Aktulga, H.  Metin, Yang, Chao, Ng, Esmond G., Maris, Pieter, and Vary, James P. Thu .  
"Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver".  United States.  https://doi.org/10.1016/j.cpc.2017.09.004.  https://www.osti.gov/servlets/purl/1439235.

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@article{osti_1439235,

  title        = {Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver},

  author       = {Shao, Meiyue and Aktulga, H.  Metin and Yang, Chao and Ng, Esmond G. and Maris, Pieter and Vary, James P.},

  abstractNote = {In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. The use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.},

  doi          = {10.1016/j.cpc.2017.09.004},

  journal      = {Computer Physics Communications},

  number       = ,

  volume       = 222,

  place        = {United States},

  year         = {Thu Sep 14 00:00:00 EDT 2017},

  month        = {Thu Sep 14 00:00:00 EDT 2017}

}

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Title: Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

Abstract

Citation Formats

Ab initio no core shell model journal, March 2013

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators journal, October 1950

Improving the scalability of a symmetric iterative eigensolver for multi-core platforms: IMPROVING THE SCALABILITY OF A SYMMETRIC ITERATIVE EIGENSOLVER journal, September 2013

Minimization Principles for the Linear Response Eigenvalue Problem II: Computation journal, January 2013

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An indefinite variant of LOBPCG for definite matrix pencils journal, August 2013

Factorization in large-scale many-body calculations journal, December 2013

The Shell-Model Code NuShellX@MSU journal, June 2014

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations journal, June 2017

Methods of conjugate gradients for solving linear systems journal, December 1952

A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems journal, April 1996

Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell journal, November 2015

A geometric theory for preconditioned inverse iteration I: Extrema of the Rayleigh quotient journal, January 2001

A geometric theory forpreconditioned inverse iterationII: Convergence estimates journal, January 2001

Krylov subspace methods for solving large unsymmetric linear systems journal, September 1981

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems journal, July 1986

Reducing the profile of sparse symmetric matrices journal, December 1976

Basis selection in LOBPCG journal, October 2006

Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method journal, January 2001

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators journal, October 1950

Methods of conjugate gradients for solving linear systems journal, December 1952

Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces journal, February 2019

Ab initio calculations of p -shell nuclei up to N 2 LO in chiral Effective Field Theory journal, July 2019

Experimental study of the low-lying negative-parity states in Be 11 using the B 12 ( d , He 3 ) Be 11 reaction journal, December 2019

Effective interactions in the s d shell journal, November 2019

Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces text, January 2018

Effective interactions in the sd shell text, January 2019

Model Order Reduction Algorithm for Estimating the Absorption Spectrum journal, September 2017

Ab initio no core shell model
journal, March 2013

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
journal, October 1950

Improving the scalability of a symmetric iterative eigensolver for multi-core platforms: IMPROVING THE SCALABILITY OF A SYMMETRIC ITERATIVE EIGENSOLVER
journal, September 2013

Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
journal, January 2013

Adaptively Compressed Exchange Operator for Large-Scale Hybrid Density Functional Calculations with Applications to the Adsorption of Water on Silicene
journal, February 2017

An indefinite variant of LOBPCG for definite matrix pencils
journal, August 2013

Factorization in large-scale many-body calculations
journal, December 2013

The Shell-Model Code NuShellX@MSU
journal, June 2014

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations
journal, June 2017

Methods of conjugate gradients for solving linear systems
journal, December 1952

A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
journal, April 1996

Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell
journal, November 2015

A geometric theory for preconditioned inverse iteration I: Extrema of the Rayleigh quotient
journal, January 2001

A geometric theory forpreconditioned inverse iterationII: Convergence estimates
journal, January 2001

Krylov subspace methods for solving large unsymmetric linear systems
journal, September 1981

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986

Reducing the profile of sparse symmetric matrices
journal, December 1976

Basis selection in LOBPCG
journal, October 2006

Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
journal, January 2001

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
journal, October 1950

Methods of conjugate gradients for solving linear systems
journal, December 1952

Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces
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Ab initio calculations of p -shell nuclei up to N ² LO in chiral Effective Field Theory
journal, July 2019

Experimental study of the low-lying negative-parity states in ${}^{11}{Be}$ using the ${}^{12}B (d, {}^{3}{He}) {}^{11}{Be}$ reaction
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Effective interactions in the $s d$ shell
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Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces
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Effective interactions in the sd shell
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Model Order Reduction Algorithm for Estimating the Absorption Spectrum
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