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A massively parallel order-N electronic structure theory was constructed byan interdisciplinary research between physics, applied mathematics and computerscience. (1) A high parallel efficiency with ten-million-atom nanomaterials wasrealized on the K computer with upto 98,304 processor cores. The mathematicalfoundation is a novel linear algebraic algorithm for the generalized shiftedlinear equation. The calculation was carried out by our code ' ELSES '(www.elses.jp) with modelled (tight-binding-form) systems based on ab initiocalculations. (2) A post-calculation analysis method, called pi-orbitalcrystalline orbital Hamiltonian population (pi-COHP) method, is presented,since the method is ideal for huge electronic structure data distributed amongmassive nodes. The analysis method is demonstrated in an sp2-sp3 nano-compositecarbon solid, with an original visualization software 'VisBAR'. The presentresearch indicates general aspects of computational physics with current ornext-generation supercomputers.

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