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Title: Solving Coupled Cluster Equations by the Newton Krylov Method

Abstract

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); Czech Science Foundation
OSTI Identifier:
1734948
Alternate Identifier(s):
OSTI ID: 1755915
Report Number(s):
PNNL-SA-155068
Journal ID: ISSN 2296-2646; 590184
Grant/Contract Number:  
AC05-76RL01830; AC05-00OR22725; 17-SC-20-SC; 19-13126Y
Resource Type:
Published Article
Journal Name:
Frontiers in Chemistry
Additional Journal Information:
Journal Name: Frontiers in Chemistry Journal Volume: 8; Journal ID: ISSN 2296-2646
Publisher:
Frontiers Research Foundation
Country of Publication:
Switzerland
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; couple cluster approximation; Newton-Krylov method; DIIS; precondition; nonlinear solver; coupled cluster; applied math; solvers

Citation Formats

Yang, Chao, Brabec, Jiri, Veis, Libor, Williams-Young, David B., and Kowalski, Karol. Solving Coupled Cluster Equations by the Newton Krylov Method. Switzerland: N. p., 2020. Web. https://doi.org/10.3389/fchem.2020.590184.
Yang, Chao, Brabec, Jiri, Veis, Libor, Williams-Young, David B., & Kowalski, Karol. Solving Coupled Cluster Equations by the Newton Krylov Method. Switzerland. https://doi.org/10.3389/fchem.2020.590184
Yang, Chao, Brabec, Jiri, Veis, Libor, Williams-Young, David B., and Kowalski, Karol. Thu . "Solving Coupled Cluster Equations by the Newton Krylov Method". Switzerland. https://doi.org/10.3389/fchem.2020.590184.
@article{osti_1734948,
title = {Solving Coupled Cluster Equations by the Newton Krylov Method},
author = {Yang, Chao and Brabec, Jiri and Veis, Libor and Williams-Young, David B. and Kowalski, Karol},
abstractNote = {We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.},
doi = {10.3389/fchem.2020.590184},
journal = {Frontiers in Chemistry},
number = ,
volume = 8,
place = {Switzerland},
year = {2020},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.3389/fchem.2020.590184

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