  A massively parallel order-N electronic structure theory was constructed by
an 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 upto 98,304 processor cores. The mathematical
foundation is a novel linear algebraic algorithm for the generalized shifted
linear equation. The calculation was carried out by our code ' ELSES '
(www.elses.jp) with modelled (tight-binding-form) systems based on ab initio
calculations. (2) A post-calculation analysis method, called pi-orbital
crystalline orbital Hamiltonian population (pi-COHP) method, is presented,
since the method is ideal for huge electronic structure data distributed among
massive nodes. The analysis method is demonstrated in an sp2-sp3 nano-composite
carbon solid, with an original visualization software 'VisBAR'. The present
research indicates general aspects of computational physics with current or
next-generation supercomputers.
