Recent developments and applications of the real-space multigrid method

Abstract

The salient features of the real-space multigrid method and its recent applications are described. This method is suitable for very large scale, massively parallel calculations of atomic and electronic structure, as well as quantum molecular dynamics. Its nearly O(N) implementation provides a compact, variationally optimized basis that is also very useful for fully O(N) calculations of quantum transport. Recently, we also developed a hybrid method for simulating biomolecules in solution, in which most of the solvent is inexpensively treated using an approximate density-functional method, while the biomolecule and its first solvation shells are described at the full Kohn–Sham level. Our calculations show excellent parallel efficiency and scaling on massively parallel supercomputers.