Efficient and Structure-Preserving Numerical Schemes for Kohn-Sham Gradient Flow Models

Abstract

This dissertation presents efficient and structure-preserving numerical schemes for calculating the electronic structure via the Kohn-Sham density functional theory (DFT) and gradient flow models. The efficiency relies on the numerical scheme’s unconditional energy stability, orbital-wise splitting design, and linearity. The structure-preserving property refers to both energy stability and orthonormality-preserving. The corresponding theoretical analysis is rigorously conducted and presented. Various numerical examples are performed to show the schemes’ effectiveness and robustness. 

Brief Biography

Xiuping Wang is a Ph.D. candidate in the Computational Transport Phenomena Lab and Scientific Computing and Machine Learning Lab at King Abdullah University of Science and Technology (KAUST). His research interests include designing robust and efficient numerical algorithms for electronic structure calculation and fluid flow in porous media.