The local ensemble transform Kalman filter (LETKF) with an intermediate atmospheric general circulation model (AGCM) is implemented with the Japanese 10 petaflops (floating point operations per second) "K computer" for large-ensemble simulations of 10,240 members, 2 orders of magnitude greater than the typical ensemble size of about 100. The computational challenge includes the eigenvalue decomposition of 10,240 × 10,240 dense covariance matrices at each grid point. Using the efficient eigenvalue solver for the K computer, the LETKF computations are accelerated by a factor of 8, allowing a 3 week experiment of 10,240-member LETKF with an intermediate AGCM for the first time. The flow-dependent 10,240-member ensemble revealed meaningful long-range error correlations at continental scales. The surface pressure error correlation shows teleconnection patterns like the Pacific North American pattern. Specific humidity error correlation shows continental scale wave trains. Investigations with different ensemble sizes suggest that at least several hundred members be necessary to capture these continental scale error correlations.

For current supercomputer systems, multicore and multisocket processors are required in order to build a system, and choice of interconnection is essential. In addition, for effective development of new code, high-performance, scalable, and reliable numerical software is key. ScaLAPACK and PETSc are software developed for distributed memory parallel computer systems. Real computation requires software that is highly tuned for implementation on new architectures, such as many-core processors.In the present study, we introduce a high-performance, highly scalable eigenvalue solver with the goal of realizing the K-computer system, which is a next-generation supercomputer system. We have developed two versions of this eigenvalue solver, namely, the standard version (eigen_s) and an enhanced-performance version (eigen_sx), both of which were developed on the T2K cluster system housed at the University of Tokyo. Eigen_s uses conventional algorithms, such as Householder tridiagonalization, the divide and conquer (DC) algorithm, and the Householder backtransformation. These algorithms are carefully implemented using a blocking technique and flexible two-dimensional data-distribution in order to reduce the overhead of memory traffic and data transfer, respectively. Eigen_s performs excellently on the T2K system with 4,096 cores (theoretical peak: 37.6 TFLOPS) and exhibits fine performance (3.0 TFLOPS) with a 200,000-dimensional matrix. The enhanced version, eigen_sx, uses more advanced algorithms, such as the narrow-band reduction algorithm, DC for band matrices, and the block Householder back-transformation with WY-representation. Even though this version is still in the test stage, eigen_sxhas realized 4.7 TFLOPS with a 200,000-dimensional matrix.

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The nitrogen K-shell X-ray absorption spectra of the purine bases present in nucleic acids, adenine and guanine, were analyzed by using ab initio Hartree-Fock static exchange and restrictedactive-space self-consistent-field calculations. A variety of derivative molecules were calculated to investigate the energetic shifts due to environmental effects on the nitrogen atoms. Shake-up excitations were also addressed.

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Abstract. In this paper, we present a communication library which extends an MPI application on a single parallel machine to a cluster of parallel machines. Stampi provides some functionality which are required for constructing distributed applications and environments based on the MPI2 standard with a focus on dynamic process management. Since the mechanism of communication bridge is transparent for users, it is very useful to assemble and link MPI applications on meta-computer systems. Furthermore Stampi supports novel functions; one is the communication between a Java applet to the backend parallel computer. Another is supporting remote file-IO. Both give us a framework of distributed resource management based on an MPI communication infrastructure. This paper covers the architecture of Stampi.

This paper proposes a method for implementing dense matrix multiplication on FP64 (DGEMM) and FP32 (SGEMM) using Tensor Cores on NVIDIA's graphics processing units (GPUs). Tensor Cores are special processing units that perform 4 × 4 matrix multiplications on FP16 inputs with FP32 precision, and return the result on FP32. The proposed method adopts the Ozaki scheme, an accurate matrix multiplication algorithm based on error-free transformation for matrix multiplication. The proposed method has three prominent advantages: first, it can be built upon the cublasGemmEx routine using Tensor Core operations; second, it can achieve higher accuracy than standard DGEMM, including the correctly-rounded result; third, it ensures bit-level reproducibility even for different numbers of cores and threads. The achievable performance of the method depends on the absolute-value range of each element of the input matrices. For example, when the matrices were initialized with random numbers over a dynamic range of 1E+9, our DGEMM-equivalent implementation achieved up to approximately 980 GFlops of FP64 operation on the Titan RTX GPU (with 130 TFlops on Tensor Cores), although cublasDgemm can achieve only 539 GFlops on FP64 floating-point units. Our results reveal the possibility of utilizing hardware with limited FP32/FP64 resources and fast low-precision processing units (such as AI-oriented processors) for general-purpose workloads. Keywords: Tensor cores • FP16 • Half-precision • Low-precision • Matrix multiplication • GEMM • Linear algebra • Accuracy • Reproducibility

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