High-order finite element method for atomic structure calculations

Čertík, Ondřej; Pask, John E.; Fernando, Isuru; Goswami, Rohit; Sukumar, N.; Collins, Lee. A.; Manzini, Gianmarco; Vackář, Jiří

doi:10.1016/j.cpc.2023.109051

High-order finite element method for atomic structure calculations

Journal Article · 14 December 2023 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2023.109051· OSTI ID:2259202

Čertík, Ondřej ^[1]; Pask, John E. ^[2]; Fernando, Isuru ^[3]; ^[4]; Sukumar, N. ^[5]; Collins, Lee. A. ^[6]; Manzini, Gianmarco ^[6]; Vackář, Jiří ^[7]

GSI Technology, Sunnyvale, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); University of Iceland and Quansight Labs
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
University of Iceland, Reykjavík (Iceland); Quansight Labs, Austin, TX (United States)
Univ. of California, Davis, CA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Czech Academy of Sciences (CAS) (Czech Republic)

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. Here, to address the slow convergence of the $κ=±1$ states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10^-8 Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schrödinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

View Accepted Manuscript (DOE)

Research Organization:: University of Iceland, Reykjavik (Iceland); Quansight Labs, Austin, TX (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344; AC52-06NA25396

OSTI ID:: 2259202

Alternate ID(s):: OSTI ID: 2331531
OSTI ID: 2440191
OSTI ID: 2246696

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 297; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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High-order finite element method for atomic structure calculations

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