Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Roh, Dong Min; Lee, Dean; Maris, Pieter; Ng, Esmond; Vary, James P.; Yang, Chao

doi:10.1016/j.jcp.2025.113921

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Journal Article · Fri Mar 14 00:00:00 EDT 2025 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2025.113921· OSTI ID:3011535

^[1]; Lee, Dean ^[2]; Maris, Pieter ^[3]; Ng, Esmond ^[1]; Vary, James P. ^[3]; Yang, Chao ^[1]

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Michigan State Univ., East Lansing, MI (United States)
Iowa State Univ., Ames, IA (United States)

Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.

View Accepted Manuscript (DOE)

Research Organization:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)

Grant/Contract Number:: SC0024586; SC0023495; SC0023175; AC02-05CH11231; SC0023658; SC0013365; SC0023692

OSTI ID:: 3011535

Alternate ID(s):: OSTI ID: 2553899
OSTI ID: 2895237

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 531; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (29)

Improving the scalability of a symmetric iterative eigensolver for multi-core platforms: IMPROVING THE SCALABILITY OF A SYMMETRIC ITERATIVE EIGENSOLVER Aktulga, Hasan Metin; Yang, Chao; Ng, Esmond G. Concurrency and Computation: Practice and Experience, Vol. 26, Issue 16 https://doi.org/10.1002/cpe.3129	journal	September 2013
A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors Hernandez, Taylor M.; Van Beeumen, Roel; Caprio, Mark A. Numerical Linear Algebra with Applications, Vol. 28, Issue 2 https://doi.org/10.1002/nla.2341	journal	October 2020
Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell Argentati, Merico E.; Knyazev, Andrew V.; Neymeyr, Klaus Foundations of Computational Mathematics, Vol. 17, Issue 3 https://doi.org/10.1007/s10208-015-9297-1	journal	November 2015
Block Krylov–Schur method for large symmetric eigenvalue problems Zhou, Yunkai; Saad, Yousef Numerical Algorithms, Vol. 47, Issue 4 https://doi.org/10.1007/s11075-008-9192-9	journal	March 2008
Convergence acceleration of iterative sequences. the case of scf iteration Pulay, Péter Chemical Physics Letters, Vol. 73, Issue 2 https://doi.org/10.1016/0009-2614(80)80396-4	journal	July 1980
The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices Davidson, Ernest R. Journal of Computational Physics, Vol. 17, Issue 1 https://doi.org/10.1016/0021-9991(75)90065-0	journal	January 1975
Davidson's method and preconditioning for generalized eigenvalue problems Morgan, Ronald B. Journal of Computational Physics, Vol. 89, Issue 1 https://doi.org/10.1016/0021-9991(90)90124-J	journal	July 1990
Numerics of Gram-Schmidt orthogonalization Björck, Å. Linear Algebra and its Applications, Vol. 197-198 https://doi.org/10.1016/0024-3795(94)90493-6	journal	January 1994
Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver Shao, Meiyue; Aktulga, H. Metin; Yang, Chao Computer Physics Communications, Vol. 222 https://doi.org/10.1016/j.cpc.2017.09.004	journal	January 2018
Hybrid eigensolvers for nuclear configuration interaction calculations Alperen, Abdullah; Aktulga, Hasan Metin; Maris, Pieter Computer Physics Communications, Vol. 292 https://doi.org/10.1016/j.cpc.2023.108888	journal	November 2023
Accelerating an iterative eigensolver for nuclear structure configuration interaction calculations on GPUs using OpenACC Maris, Pieter; Yang, Chao; Oryspayev, Dossay Journal of Computational Science, Vol. 59 https://doi.org/10.1016/j.jocs.2021.101554	journal	March 2022
N3LO NN interaction adjusted to light nuclei in ab exitu approach Shirokov, A. M.; Shin, I. J.; Kim, Y. Physics Letters B, Vol. 761 https://doi.org/10.1016/j.physletb.2016.08.006	journal	October 2016
Ab initio no core shell model Barrett, Bruce R.; Navrátil, Petr; Vary, James P. Progress in Particle and Nuclear Physics, Vol. 69 https://doi.org/10.1016/j.ppnp.2012.10.003	journal	March 2013
Scaling of ab-initio nuclear physics calculations on multicore computer architectures Maris, Pieter; Sosonkina, Masha; Vary, James P. Procedia Computer Science, Vol. 1, Issue 1 https://doi.org/10.1016/j.procs.2010.04.012	journal	May 2010
On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations I Fan, Ky Proceedings of the National Academy of Sciences, Vol. 35, Issue 11 https://doi.org/10.1073/pnas.35.11.652	journal	November 1949
A new method for diagonalising large matrices Wood, D. M.; Zunger, A. Journal of Physics A: Mathematical and General, Vol. 18, Issue 9 https://doi.org/10.1088/0305-4470/18/9/018	journal	June 1985
An analysis of the Rayleigh--Ritz method for approximating eigenspaces Jia, Zhongxiao; Stewart, G. W. Mathematics of Computation, Vol. 70, Issue 234 https://doi.org/10.1090/S0025-5718-00-01208-4	journal	February 2000
An incomplete factorization technique for positive definite linear systems Manteuffel, T. A. Mathematics of Computation, Vol. 34, Issue 150 https://doi.org/10.1090/S0025-5718-1980-0559197-0	journal	May 1980
Improved many-body expansions from eigenvector continuation Demol, P.; Duguet, T.; Ekström, A. Physical Review C, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevC.101.041302	journal	April 2020
Eigenvector Continuation with Subspace Learning Frame, Dillon; He, Rongzheng; Ipsen, Ilse Physical Review Letters, Vol. 121, Issue 3 https://doi.org/10.1103/PhysRevLett.121.032501	journal	July 2018
Convergence of Eigenvector Continuation Sarkar, Avik; Lee, Dean Physical Review Letters, Vol. 126, Issue 3 https://doi.org/10.1103/PhysRevLett.126.032501	journal	January 2021
Solution of Sparse Indefinite Systems of Linear Equations Paige, C. C.; Saunders, M. A. SIAM Journal on Numerical Analysis, Vol. 12, Issue 4 https://doi.org/10.1137/0712047	journal	September 1975
Gradient Flow Approach to Geometric Convergence Analysis of Preconditioned Eigensolvers Knyazev, Andrew V.; Neymeyr, Klaus SIAM Journal on Matrix Analysis and Applications, Vol. 31, Issue 2 https://doi.org/10.1137/080727567	journal	January 2009
A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration Neymeyr, Klaus SIAM Journal on Numerical Analysis, Vol. 50, Issue 6 https://doi.org/10.1137/11084488X	journal	January 2012
A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems Sleijpen, Gerard L. G.; Van der Vorst, Henk A. SIAM Review, Vol. 42, Issue 2 https://doi.org/10.1137/S0036144599363084	journal	January 2000
A Krylov--Schur Algorithm for Large Eigenproblems Stewart, G. W. SIAM Journal on Matrix Analysis and Applications, Vol. 23, Issue 3 https://doi.org/10.1137/S0895479800371529	journal	January 2002
A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems Grimes, Roger G.; Lewis, John G.; Simon, Horst D. SIAM Journal on Matrix Analysis and Applications, Vol. 15, Issue 1 https://doi.org/10.1137/S0895479888151111	journal	January 1994
Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method Knyazev, Andrew V. SIAM Journal on Scientific Computing, Vol. 23, Issue 2 https://doi.org/10.1137/S1064827500366124	journal	January 2001
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators Lanczos, C. Journal of Research of the National Bureau of Standards, Vol. 45, Issue 4 https://doi.org/10.6028/jres.045.026	journal	October 1950

Similar Records

Hybrid eigensolvers for nuclear configuration interaction calculations

Journal Article · Mon Aug 07 00:00:00 EDT 2023 · Computer Physics Communications · OSTI ID:2439952

Related Subjects

Eigenpair approximations
Nuclear structure calculations
Perturbative corrections
Rayleigh-Schrödinger perturbation theory
Subspace projection

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Citation Formats

References (29)

Similar Records

Related Subjects