Convergence study of isogeometric analysis based on Bézier extraction in electronic structure calculations

Behavior of various, even hypothetical, materials can be predicted via ab-initio electronic structure calculations providing all the necessary information: the total energy of the system and its derivatives. In case of non-periodic structures, the existing well-established methods for electronic structure calculations either use special bases, predetermining and limiting the shapes of wave functions, or require artificial computationally expensive arrangements, like large supercells. We developed a new method for non-periodic electronic structures based on the density functional theory, environment-reflecting pseudopotentials and the isogeometric analysis with Bézier extraction, ensuring continuity for all quantities up to the second derivative. The approach is especially suitable for calculating the total energy derivatives and for molecular-dynamics simulations. Its main assets are the universal basis with the excellent convergence control and the capability to calculate precisely the non-periodic structures even lacking in charge neutrality. Within the present paper, convergence study for isogeometric analysis vs. standard finite-element approach is carried out and illustrated on sub-problems that appear in our electronic structure calculations method: the Poisson problem, the generalized eigenvalue problem and the density functional theory Kohn-Sham equations applied to a benchmark problem.