A Space-filling Curve Based Grid Partition to Accelerate Real-space Pseudopotential Density Functional Theory Calculations

Density functional theory (DFT) has become a popular tool to verify, explain, and predict experimental discoveries in materials. In conjunction with pseudopotentials, we can now achieve simulations of systems with tens of thousands of atoms as “routine work.” Real-space DFT has advantages when simulating confined or semi-periodic systems, such as defects, charged systems, and interfaces. Within a finite-difference method, the Hamiltonian matrix is often large and sparse, and requires an efficient implementation of matrix-vector multiplication. We will show through space-filling curves that we can construct a real-space grid whose grid points have excellent locality. Consequently, the communication between compute nodes is reduced. We will also demonstrate that this space-filling curve based grid partition improves the scalability of the matrix-vector multiplications, which is beneficial to polynomial filtering based eigensolvers.