Ten-million-atom electronic structure calculations on the K computer with a massively parallel order-N theory

摘要

A massively parallel order-N electronic structure theory was developed by interdisciplinary research between physics, applied mathematics, and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was realized on the K computer with up to 98,304 processor cores. The mathematical foundation is a novel linear algebraic algorithm for generalized shifted linear equations. The calculation was carried out using our code "ELSES" (www.elses.jp) with modelled (tight-binding-form) systems based on ab initio calculations. (2) A postcalculation analysis method, called the π-orbital crystalline orbital Hamiltonian population (π-COHP) method, is presented, since this method is ideal for huge electronic structure data distributed among massive nodes. The analysis method is demonstrated in an sp~2-sp~3 nanocomposite carbon solid, with the original visualization software "VisBAR". The present research indicates the general aspects of computational physics with current or next-generation supercomputers.