Space-filling Curves for Real-space Pseudopotential Density Functional Theory Calculations

Pseudopotential density functional theory is a popular approach to predict material properties and to explain experimental observations. With this approach implemented in real space, we are able to simulate systems of tens of thousands of atoms as routine work. Real-space methods discretize the simulation domain and are advantageous when simulating confined or semi-periodic systems, such as charged defects and interfaces. Among real-space methods, finite difference methods are easier to implement. The Hamiltonian matrix is often large but sparse, which requires an efficient implementation of matrix–vector multiplications. Using space-filling curves, we can construct a real-space grid with excellent locality. Consequently, the communication overhead can be reduced and is more balanced. We will also demonstrate the improved scalability of the matrix–vector multiplications, which is beneficial to polynomial filtering based eigensolvers.