Real time time-dependent density functional theory using higher order finite-element methods

Journal Article · 23 September 2019 · Physical Review. B

DOI: https://doi.org/10.1103/PhysRevB.100.115148 · OSTI ID:1564082

Kanungo, Bikash ^[1]; Gavini, Vikram ^[2]

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1. Univ. of Michigan, Ann Arbor, MI (United States); University of Michigan
2. Univ. of Michigan, Ann Arbor, MI (United States)

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real time using higher order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this end, we develop an a priori mesh adaption technique, based on the semidiscrete (discrete in space but continuous in time) error estimate on the time-dependent Kohn-Sham orbitals, to construct an efficient finite-element discretization. Subsequently, we obtain the full-discrete error estimate to guide our choice of the time step. We employ spectral finite elements along with special reduced order quadrature to render the overlap matrix diagonal, thereby simplifying the inversion of the overlap matrix that features in the evaluation of the discrete time-evolution operator. We use the second-order Magnus operator as the time-evolution operator, wherein the action of the discrete Magnus operator, expressed as exponential of a matrix, on the Kohn-Sham orbitals is obtained efficiently through an adaptive Lanczos iteration. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization, for both pseudopotential and all-electron calculations. We demonstrate a staggering 100-fold reduction in the computational time afforded by higher order finite elements over linear finite elements, for both pseudopotential and all-electron calculations. Further, for similar level of accuracy, we obtain significant computational savings by our approach as compared to state-of-the-art finite-difference methods. Here, we also demonstrate the competence of higher order finite elements for all-electron benchmark systems. Lastly, we observe good parallel scalability of the proposed method on many hundreds of processors.

• Research Organization: Univ. of Michigan, Ann Arbor, MI (United States); University of Michigan, Ann Arbor, MI (United States)
• Sponsoring Organization: Army Research Office; National Science Foundation; USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: AC02-05CH11231; SC0017380
• OSTI ID: 1564082
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 11 Vol. 100; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English