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The standardization of an interface for dense linear algebra operations in the BLAS standard has enabled interoperability between different linear algebra libraries, thereby boosting the success of scientific computing, in particular in scientific HPC. Despite numerous efforts in the past, the community has not yet agreed on a standardization for sparse linear algebra operations due to numerous reasons. One is the fact that sparse linear algebra objects allow for many different storage formats, and different hardware may favor different storage formats. This makes the definition of a FORTRAN-style all-circumventing interface extremely challenging. Another reason is that opposed to dense linear algebra functionality, in sparse linear algebra, the size of the sparse data structure for the operation result is not always known prior to the information. Furthermore, as opposed to the standardization effort for dense linear algebra, we are late in the technology readiness cycle, and many production-ready software libraries using sparse linear algebra routines have implemented and committed to their own sparse BLAS interface. At the same time, there exists a demand for standardization that would improve interoperability, and sustainability, and allow for easier integration of building blocks. In an inclusive, cross-institutional effort involving numerous academic institutions, US National Labs, and industry, we spent two years designing a hardware-portable interface for basic sparse linear algebra functionality that serves the user needs and is compatible with the different interfaces currently used by different vendors. In this paper, we present a C++ API for sparse linear algebra functionality, discuss the design choices, and detail how software developers preserve a lot of freedom in terms of how to implement functionality behind this API., Comment: 43 pages

In order to understand cardiac arrhythmia, computer models for electrophysiology are essential. In the EuroHPC MicroCARD project, we adapt the current models and leverage modern computing resources to model diseased hearts and their microstructure accurately. Towards this objective, we develop a portable, highly efficient, and performing BDDC preconditioner and solver implementation, demonstrating scalability with over 90% efficiency on up to 100 GPUs.

With the announcement that the Aurora Supercomputer will be composed of general purpose Intel CPUs complemented by discrete high performance Intel GPUs, and the deployment of the oneAPI ecosystem, Intel has committed to enter the arena of discrete high performance GPUs. A central requirement for the scientific computing community is the availability of production-ready software stacks and a glimpse of the performance they can expect to see on Intel high performance GPUs. In this paper, we present the first platform-portable open source math library supporting Intel GPUs via the DPC++ programming environment. We also benchmark some of the developed sparse linear algebra functionality on different Intel GPUs to assess the efficiency of the DPC++ programming ecosystem to translate raw performance into application performance. Aside from quantifying the efficiency within the hardware-specific roofline model, we also compare against routines providing the same functionality that ship with Intel's oneMKL vendor library., Comment: preprint, not submitted

The first associations to software sustainability might be the existence of a continuous integration (CI) framework; the existence of a testing framework composed of unit tests, integration tests, and end-to-end tests; and also the existence of software documentation. However, when asking what is a common deathblow for a scientific software product, it is often the lack of platform and performance portability. Against this background, we designed the Ginkgo library with the primary focus on platform portability and the ability to not only port to new hardware architectures, but also achieve good performance. In this paper we present the Ginkgo library design, radically separating algorithms from hardware-specific kernels forming the distinct hardware executors, and report our experience when adding execution backends for NVIDIA, AMD, and Intel GPUs. We also comment on the different levels of performance portability, and the performance we achieved on the distinct hardware backends., Comment: Submitted to Parallel Computing Journal (PARCO)

GPU accelerators have become an important backbone for scientific high performance computing, and the performance advances obtained from adopting new GPU hardware are significant. In this paper we take a first look at NVIDIA's newest server line GPU, the A100 architecture part of the Ampere generation. Specifically, we assess its performance for sparse linear algebra operations that form the backbone of many scientific applications and assess the performance improvements over its predecessor.

Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the server-line products are increasingly featuring low-precision special function units, such as the NVIDIA tensor cores in ORNL's Summit supercomputer providing more than an order of magnitude higher performance than what is available in IEEE double precision. At the same time, the gap between the compute power on the one hand and the memory bandwidth on the other hand keeps increasing, making data access and communication prohibitively expensive compared to arithmetic operations. To start the multiprecision focus effort, we survey the numerical linear algebra community and summarize all existing multiprecision knowledge, expertise, and software capabilities in this landscape analysis report. We also include current efforts and preliminary results that may not yet be considered "mature technology," but have the potential to grow into production quality within the multiprecision focus effort. As we expect the reader to be familiar with the basics of numerical linear algebra, we refrain from providing a detailed background on the algorithms themselves but focus on how mixed- and multiprecision technology can help improving the performance of these methods and present highlights of application significantly outperforming the traditional fixed precision methods., Comment: Technical report as a part of the Exascale computing project (ECP)

In this paper, we present Ginkgo, a modern C++ math library for scientific high performance computing. While classical linear algebra libraries act on matrix and vector objects, Ginkgo's design principle abstracts all functionality as "linear operators", motivating the notation of a "linear operator algebra library". Ginkgo's current focus is oriented towards providing sparse linear algebra functionality for high performance GPU architectures, but given the library design, this focus can be easily extended to accommodate other algorithms and hardware architectures. We introduce this sophisticated software architecture that separates core algorithms from architecture-specific back ends and provide details on extensibility and sustainability measures. We also demonstrate Ginkgo's usability by providing examples on how to use its functionality inside the MFEM and deal.ii finite element ecosystems. Finally, we offer a practical demonstration of Ginkgo's high performance on state-of-the-art GPU architectures., Comment: Preprint submitted to ACM Transactions on Mathematical Software

With AMD reinforcing their ambition in the scientific high performance computing ecosystem, we extend the hardware scope of the Ginkgo linear algebra package to feature a HIP backend for AMD GPUs. In this paper, we report and discuss the porting effort from CUDA, the extension of the HIP framework to add missing features such as cooperative groups, the performance price of compiling HIP code for AMD architectures, and the design of a library providing native backends for NVIDIA and AMD GPUs while minimizing code duplication by using a shared code base., Comment: Preprint submitted to HeteroPar

With the commencement of the exascale computing era, we realize that the majority of the leadership supercomputers are heterogeneous and massively parallel even on a single node with multiple co-processors such as GPUs and multiple cores on each node. For example, ORNLs Summit accumulates six NVIDIA Tesla V100s and 42 core IBM Power9s on each node. Synchronizing across all these compute resources in a single node or even across multiple nodes is prohibitively expensive. Hence it is necessary to develop and study asynchronous algorithms that circumvent this issue of bulk-synchronous computing for massive parallelism. In this study, we examine the asynchronous version of the abstract Restricted Additive Schwarz method as a solver where we do not explicitly synchronize, but allow for communication of the data between the sub-domains to be completely asynchronous thereby removing the bulk synchronous nature of the algorithm. We accomplish this by using the onesided RMA functions of the MPI standard. We study the benefits of using such an asynchronous solver over its synchronous counterpart on both multi-core architectures and on multiple GPUs. We also study the communication patterns and local solvers and their effect on the global solver. Finally, we show that this concept can render attractive runtime benefits over the synchronous counterparts., Comment: Preprint submitted to IJHPCA