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arXiv · 1512.07156

Finite element method and isogeometric analysis in electronic structure calculations: convergence study

Robert Cimrman·Matyáš Novák·Radek Kolman·Miroslav Tůma·Jiří Vackář
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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.

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Robert Cimrman, Matyáš Novák, Radek Kolman, Miroslav Tůma, Jiří Vackář. 2015-12-22. Finite element method and isogeometric analysis in electronic structure calculations: convergence study. https://doi.org/10.1016/j.amc.2017.02.023

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