Partition of unity finite element method for quantum mechanical materials calculations

Pask, J. E.; Sukumar, N.

doi:10.1016/j.eml.2016.11.003

Title: Partition of unity finite element method for quantum mechanical materials calculations

Journal Article · Wed Nov 09 00:00:00 EST 2016 · Extreme Mechanics Letters

DOI:https://doi.org/10.1016/j.eml.2016.11.003· OSTI ID:1438699

Pask, J. E. ^[1]; Sukumar, N. ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of California, Davis, CA (United States)

The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences (FD) and finite-elements (FE) have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative to PW: excessive number of degrees of freedom (basis functions) needed to achieve the required accuracies. In this paper, we present a real-space partition of unity finite element (PUFE) method to solve the Kohn–Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution process using partition-of-unity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to metals and insulators alike, and particularly efficient for deep, localized potentials, as occur in calculations at extreme conditions of pressure and temperature. Full self-consistent Kohn–Sham calculations are presented for LiH, involving light atoms, and CeAl, involving heavy atoms with large numbers of atomic-orbital enrichments. We find that the new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. As a result, we compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to obtain.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1438699

Alternate ID(s):: OSTI ID: 1398695

Report Number(s):: LLNL-JRNL-716258

Journal Information:: Extreme Mechanics Letters, Vol. 11, Issue C; ISSN 2352-4316

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 17 works

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Title: Partition of unity finite element method for quantum mechanical materials calculations

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