Finite element method and isogeometric analysis in electronic structure calculations: convergence study
Computational Physics
2021-01-07 v1 Numerical Analysis
Quantum Physics
Abstract
We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The convergence is studied on simple sub-problems that appear within the density functional theory approximation to the Schr\"odinger equation: the Poisson problem and the generalized eigenvalue problem. We also outline the complete iterative algorithm seeking a fixed point of the charge density of a system of atoms or molecules, and study IGA/FEM convergence on a benchmark problem of nitrogen atom.
Keywords
Cite
@article{arxiv.1512.07156,
title = {Finite element method and isogeometric analysis in electronic structure calculations: convergence study},
author = {Robert Cimrman and Matyáš Novák and Radek Kolman and Miroslav Tůma and Jiří Vackář},
journal= {arXiv preprint arXiv:1512.07156},
year = {2021}
}