Inner product computation for sparse iterative solvers on\ud distributed supercomputer

Recent years have witnessed that iterative Krylov methods without re-designing are not suitable for distribute supercomputers because of intensive global communications. It is well accepted that re-engineering Krylov methods for prescribed computer architecture is necessary and important to achieve higher performance and scalability. The paper focuses on simple and practical ways to re-organize Krylov methods and improve their performance for current heterogeneous distributed supercomputers. In construct with most of current software development of Krylov methods which usually focuses on efficient matrix vector multiplications, the paper focuses on the way to compute inner products on supercomputers and explains why inner product computation on current heterogeneous distributed supercomputers is crucial for scalable Krylov methods. Communication complexity analysis shows that how the inner product computation can be the bottleneck of performance of (inner) product-type iterative solvers on distributed supercomputers due to global communications. Principles of reducing such global communications are discussed. The importance of minimizing communications is demonstrated by experiments using up to 900 processors. The experiments were carried on a Dawning 5000A, one of the fastest and earliest heterogeneous supercomputers in the world. Both the analysis and experiments indicates that inner product computation is very likely to be the most challenging kernel for inner product-based iterative solvers to achieve exascale

A review of High Performance Computing foundations for scientists

The increase of existing computational capabilities has made simulation emerge as a third discipline of Science, lying midway between experimental and purely theoretical branches [1, 2]. Simulation enables the evaluation of quantities which otherwise would not be accessible, helps to improve experiments and provides new insights on systems which are analysed [3-6]. Knowing the fundamentals of computation can be very useful for scientists, for it can help them to improve the performance of their theoretical models and simulations. This review includes some technical essentials that can be useful to this end, and it is devised as a complement for researchers whose education is focused on scientific issues and not on technological respects. In this document we attempt to discuss the fundamentals of High Performance Computing (HPC) [7] in a way which is easy to understand without much previous background. We sketch the way standard computers and supercomputers work, as well as discuss distributed computing and discuss essential aspects to take into account when running scientific calculations in computers.Comment: 33 page

Pseudorandom number generation on supercomputers

Random Walks;Supercomputer;computer science

TensorFlow Doing HPC

TensorFlow is a popular emerging open-source programming framework supporting the execution of distributed applications on heterogeneous hardware. While TensorFlow has been initially designed for developing Machine Learning (ML) applications, in fact TensorFlow aims at supporting the development of a much broader range of application kinds that are outside the ML domain and can possibly include HPC applications. However, very few experiments have been conducted to evaluate TensorFlow performance when running HPC workloads on supercomputers. This work addresses this lack by designing four traditional HPC benchmark applications: STREAM, matrix-matrix multiply, Conjugate Gradient (CG) solver and Fast Fourier Transform (FFT). We analyze their performance on two supercomputers with accelerators and evaluate the potential of TensorFlow for developing HPC applications. Our tests show that TensorFlow can fully take advantage of high performance networks and accelerators on supercomputers. Running our TensorFlow STREAM benchmark, we obtain over 50% of theoretical communication bandwidth on our testing platform. We find an approximately 2x, 1.7x and 1.8x performance improvement when increasing the number of GPUs from two to four in the matrix-matrix multiply, CG and FFT applications respectively. All our performance results demonstrate that TensorFlow has high potential of emerging also as HPC programming framework for heterogeneous supercomputers.Comment: Accepted for publication at The Ninth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES'19