Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics

Journal article


Publication Details

Author(s): Davydov D, Gerasimov T, Pelteret JP, Steinmann P
Journal: Advanced Modeling and Simulation in Engineering Sciences
Publication year: 2017
Volume: 4
Journal issue: 1
Pages range: 7
ISSN: 2213-7467


Abstract


In this paper the h-adaptive partition-of-unity method and the h- and hp-adaptive finite element method are applied to eigenvalue problems arising in quantum mechanics, namely, the Schrödinger equation with Coulomb and harmonic potentials, and the all-electron Kohn--Sham density functional theory. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling implementation of error-controlled adaptive mesh refinement strategies. To that end, local interpolation error estimates are derived for the partition-of-unity method enriched with a class of exponential functions. The efficiency of the h-adaptive partition-of-unity method is compared to the h- and hp-adaptive finite element method. The latter is implemented by adopting the analyticity estimate from Legendre coefficients. An extension of this approach to multiple solution vectors is proposed. Numerical results confirm the theoretically predicted convergence rates and remarkable accuracy of the h-adaptive partition-of-unity approach. Implementational details of the partition-of-unity method related to enforcing continuity with hanging nodes are discussed.



FAU Authors / FAU Editors

Davydov, Denis
Lehrstuhl für Technische Mechanik
Pelteret, Jean-Paul
Lehrstuhl für Technische Mechanik
Steinmann, Paul Prof. Dr.-Ing.
Lehrstuhl für Technische Mechanik


How to cite

APA:
Davydov, D., Gerasimov, T., Pelteret, J.-P., & Steinmann, P. (2017). Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics. Advanced Modeling and Simulation in Engineering Sciences, 4(1), 7. https://dx.doi.org/10.1186/s40323-017-0093-0

MLA:
Davydov, Denis, et al. "Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics." Advanced Modeling and Simulation in Engineering Sciences 4.1 (2017): 7.

BibTeX: 

Last updated on 2018-30-11 at 14:47