Matrix-Free Locally Adaptive Finite Element Solution of Density-Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning

Davydov D, Heister T, Kronbichler M, Steinmann P (2018)

Publication Type: Journal article

Publication year: 2018

Journal

physica status solidi (b) Wiley

Book Volume: 255

Article Number: 1800069

Journal Issue: 9

DOI: 10.1002/pssb.201800069

Abstract

In this paper, we propose a new numerical method to find the ground state energy of a given physical system within the Kohn–Sham density functional theory. The h-adaptive finite element method is adopted for spatial discretization and implemented with matrix-free operator evaluation. The ground state energy is found by performing unconstrained minimization with non-orthogonal orbitals using the limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. A geometric multigrid preconditioner is applied to improve the convergence. The clear advantage of the proposed approach is demonstrated on selected examples by comparing the performance to other methods such as preconditioned steepest descent minimization. The proposed method provides a solid framework toward (Formula presented.) (N) complexity for the locally adaptive real-space solution of density functional theory with finite elements.

Authors with CRIS profile

Denis Davydov Lehrstuhl für Technische Mechanik Paul Steinmann Lehrstuhl für Technische Mechanik

Involved external institutions

Clemson University US United States (USA) (US) Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Davydov, D., Heister, T., Kronbichler, M., & Steinmann, P. (2018). Matrix-Free Locally Adaptive Finite Element Solution of Density-Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning. physica status solidi (b), 255(9). https://dx.doi.org/10.1002/pssb.201800069

MLA:

Davydov, Denis, et al. "Matrix-Free Locally Adaptive Finite Element Solution of Density-Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning." physica status solidi (b) 255.9 (2018).

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