Abstract
Higher-order finite element methods are applied to electronic structure calculation in the context of the finite element method. For this purpose, the Kohn-Sham formalism of density functional theory is cast in a setting that is amenable to a finite element discretization. Both all-electron and pseudopotential formulations are presented, the latter incorporating both local and nonlocal contributions. Some of the outstanding challenges in applying this numerical framework to such ab initio methods are discussed. Finally, the approach is demonstrated with higher-order finite element basis sets that are associated with classical Lagrange discretizations as well as more with more recent isogeometric ones based on NURBS and B-splines.
Recalling that Peter Wriggers is from Hamburg, I would like to quote what John Lennon said about this city – after adapting it to my academic life that began as a Ph.D. student: “I was born in Berkeley, but I grew up in Hannover.” I am grateful to Prof. Wriggers for many opportunities that he provided for scientific growth and I can think of no better way to thank him than to choose a topic that actually started as a hobby of sorts while I was still at his institute. I extend my best wishes to him on the occasion of his 70th birthday. –İ.T.
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Temizer, l. (2022). Higher-Order Finite Element Methods for Kohn-Sham Density Functional Theory. In: Aldakheel, F., Hudobivnik, B., Soleimani, M., Wessels, H., Weißenfels, C., Marino, M. (eds) Current Trends and Open Problems in Computational Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-87312-7_51
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