Isogeometric analysis in electronic structure calculations

Abstract

In electronic structure calculations, various material properties can be obtained by means of computing the total energy of a system as well as derivatives of the total energy w.r.t. atomic positions. The derivatives, also known as Hellman-Feynman forces, require, because of practical computational reasons, the discretized charge density and wave functions having continuous second derivatives in the whole solution domain. We describe an application of isogeometric analysis (IGA), a spline modification of finite element method (FEM), to achieve the required continuity. The novelty of our approach is in employing the technique of Bézier extraction to add the IGA capabilities to our FEM based code for ab-initio calculations of electronic states of non-periodic systems within the density-functional framework, built upon the open source finite element package SfePy. We compare FEM and IGA in benchmark problems and several numerical results are presented.

arXiv admin note: substantial text overlap with arXiv:1512.07156

References in corpus (3)

• 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
• Enhancing SfePy with Isogeometric Analysis

Cited by in corpus (2)

• Multiscale finite element calculations in Python using SfePy
• Finite element method and isogeometric analysis in electronic structure calculations: convergence study