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

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 Schrödinger 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.

References in corpus (6)

• A subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization
• SfePy - Write Your Own FE Application
• Isogeometric analysis in electronic structure calculations
• Proceedings of the 6th European Conference on Python in Science (EuroSciPy 2013)
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• On the $h$-adaptive PUM and the $hp$-adaptive FEM approaches applied to PDEs in quantum mechanics

Cited by in corpus (2)

• Multiscale finite element calculations in Python using SfePy
• On the $h$-adaptive PUM and the $hp$-adaptive FEM approaches applied to PDEs in quantum mechanics