Solving Coupled Cluster Equations by the Newton Krylov Method

Yang, Chao; Brabec, Jiri; Veis, Libor; Williams-Young, David B.; Kowalski, Karol

doi:10.3389/fchem.2020.590184

Title: Solving Coupled Cluster Equations by the Newton Krylov Method

Journal Article · 10 December 2020 · Frontiers in Chemistry

DOI: https://doi.org/10.3389/fchem.2020.590184 · OSTI ID:1734948

Yang, Chao ^[1]; Brabec, Jiri ^[2]; Veis, Libor ^[2]; Williams-Young, David B. ^[1]; Kowalski, Karol ^[3]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
Academy of Sciences, Prague (Czechia)
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

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.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); Czech Science Foundation

Grant/Contract Number:: AC05-76RL01830; AC05-00OR22725; 17-SC-20-SC; 19-13126Y

OSTI ID:: 1734948

Alternate ID(s):: OSTI ID: 1755915

Report Number(s):: PNNL-SA-155068

Journal Information:: Frontiers in Chemistry, Vol. 8; ISSN 2296-2646

Publisher:: Frontiers Research FoundationCopyright Statement

Country of Publication:: United States

Language:: English

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
couple cluster approximation
Newton-Krylov method
DIIS
precondition
nonlinear solver
coupled cluster
applied math
solvers

Title: Solving Coupled Cluster Equations by the Newton Krylov Method

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