Real space DFT (RSDFT) is a simulation technique most suitable for massively-parallel architectures to perform first-principles electronic-structure calculations based on density functional theory. We here report unprecedented simulations on the electron states of silicon nanowires with up to 107,292 atoms carried out during the initial performance evaluation phase of the K computer being developed at RIKEN.

A full electron calculation for the photosynthetic reaction center of Rhodopseudomonas viridis was performed by using the fragment molecular orbital (FMO) method on a massive cluster computer. The target system contains 20,581 atoms and 77,754 electrons, which was divided into 1,398 fragments. According to the FMO prescription, the calculations of the fragments and pairs of the fragments were conducted to obtain the electronic state of the system. The calculation at RHF/6-31G* level of theory took 72.5 hours with 600 CPUs. The CPUs were grouped into several workers, to which the calculations of the fragments were dispatched. An uneven CPU grouping, where two types of workers are generated, was shown to be efficient.

We succeeded in getting 14.9 TFLOPS performance when running a plasma simulation code IMPACT-3D parallelized with High Performance Fortran on 512 nodes of the Earth Simulator. The theoretical peak performance of the 512 nodes is 32 TFLOPS, which means 45% of the peak performance was obtained with HPF.IMPACT-3D is an implosion analysis code using TVD scheme, which performs three-dimensional compressible and inviscid Eulerian fluid computation with the explicit 5-point stencil scheme for spatial differentiation and the fractional time step for time integration. The mesh size is 2048x2048x4096, and the third dimension was distributed for the parallelization. The HPF system used in the evaluation is HPF/ES, developed for the Earth Simulator by enhancing NEC HPF/SX V2 mainly in communication scalability. Shift communications were manually tuned to get best performance by using HPF/JA extensions, which was designed to give the users more control over sophisticated parallelization and communication optimizations.

A spectral atmospheric general circulation model called AFES (AGCM for Earth Simulator) was developed and optimized for the architecture of the Earth Simulator (ES). The ES is a massively parallel vector supercomputer that consists of 640 processor nodes interconnected by a single stage crossbar network with its total peak performance of 40.96 Tflops was achieved for a high resolution simulation (T1279L96) with AFES by utilizing the full 640-node configuration of the ES. The resulting computing efficiency is 64.9% of the peak performance, well surpassing that of conventional weather/climate applications having just 25-50% efficiency even on vector parallel computers. This remarkable performance proves the effectiveness of the ES as a viable means for practical applications.

The high-resolution direct numerical simulations (DNSs) of incompressible turbulence with numbers of grid points up to 40963 have been executed on the Earth Simulator (ES). The DNSs are based on the Fourier spectral method, so that the equation for mass conservation is accurately solved. In DNS based on the spectral method, most of the computation time is consumed in calculating the three-dimensional (3D) Fast Fourier Transform (FFT), which requires huge-scale global data transfer and has been the major stumbling block that has prevented truly high-performance computing. By implementing new methods to efficiently perform the 3D-FFT on the ES, we have achieved DNS at 16.4 Tflops on 20483 grid points. The DNS yields an energy spectrum exhibiting a wide inertial subrange, in contrast to previous DNSs with lower resolutions, and therefore provides valuable data for the study of the universal features of turbulence at large Reynolds number.