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The significant presence that many-core devices like GPUs have these days, and their enormous computational power, motivates the study of sparse matrix operations in this hardware. The essential sparse kernels in scientific computing, such as the sparse matrix-vector multiplication (SpMV), usually have many different high-performance GPU implementations. Sparse matrix problems typically imply memory-bound operations, and this characteristic is particularly limiting in massively parallel processors. This work revisits the main ideas about reducing the volume of data required by sparse storage formats and advances in understanding some compression techniques. In particular, we study the use of index compression combined with sparse matrix reordering techniques in CSR and explore other approaches using a blocked format. The systematic experimental evaluation on a large set of real-world matrices confirms that this approach achieves meaningful data storage reductions. Additionally, we find promising results of the impact of the storage reduction on the execution time when using accelerators to perform the mathematical kernels.

RESUMENEn este trabajo se presentan las características del sistema global de pronóstico desarrollado para el Río de la Plata y Frente Marítimo, denominado PronUy_RPFM, y en particular la componente del pronóstico de nivel de mar disponible actualmente en tiempo real. El prototipo actual (prototipo_1) del sistema de pronóstico desarrollado está automatizado y en funcionamiento desde el año 2021, publicando resultados en tiempo real, y refiere al pronóstico de niveles de marea. El modelo numérico de base utilizado es el TELEMAC2D y es forzado con el pronóstico diario oceánico global RTOFS- HYCOM y el pronóstico meteorológico global del NCEP (NOAA), ambos con información horaria. El pronóstico de niveles es evaluado en tiempo real con datos medidos in-situ por 10 mareógrafos ubicados en al área de estudio cuyos datos están disponibles online publicados por Argentina y Uruguay y son descargados diariamente por el sistema. El modelo hidrodinámico fue calibrado en base a la modificación de los parámetros vinculados a fricción de fondo y tensión de corte superficial del viento. Como resultado el modelo ha sido ajustado y el pronóstico disponible permite predecir los niveles con buena calidad tanto en condiciones medias como en condiciones de niveles extremos altos y bajos.

The widespread adoption of massively parallel processors over the past decade has fundamentally transformed the landscape of high-performance computing hardware. This revolution has recently driven the advancement of FPGAs, which are emerging as an attractive alternative to power-hungry many-core devices in a world increasingly concerned with energy consumption. Consequently, numerous recent studies have focused on implementing efficient dense and sparse numerical linear algebra (NLA) kernels on FPGAs. To maximize the efficiency of these kernels, a key aspect is the exploration of analytical tools to comprehend the performance of the developments and guide the optimization process. In this regard, the roofline model (RLM) is a well-known graphical tool that facilitates the analysis of computational performance and identifies the primary bottlenecks of a specific software when executed on a particular hardware platform. Our previous efforts advanced in developing efficient implementations of the sparse matrix–vector multiplication (SpMV) for FPGAs, considering both speed and energy consumption. In this work, we propose an extension of the RLM that enables optimizing runtime and energy consumption for NLA kernels based on sparse blocked storage formats on FPGAs. To test the power of this tool, we use it to extend our previous SpMV kernels by leveraging a block-sparse storage format that enables more efficient data access.

The dissemination of multi-core architectures and the later irruption of massively parallel devices, led to a revolution in High-Performance Computing (HPC) platforms in the last decades. As a result, Field-Programmable Gate Arrays (FPGAs) are re-emerging as a versatile and more energy-efficient alternative to other platforms. Traditional FPGA design implies using low-level Hardware Description Languages (HDL) such as VHDL or Verilog, which follow an entirely different programming model than standard software languages, and their use requires specialized knowledge of the underlying hardware. In the last years, manufacturers started to make big efforts to provide High-Level Synthesis (HLS) tools, in order to allow a grater adoption of FPGAs in the HPC community. Our work studies the use of multi-core hardware and different FPGAs to address Numerical Linear Algebra (NLA) kernels such as the general matrix multiplication GEMM and the sparse matrix-vector multiplication SpMV. Specifically, we compare the behavior of fine-tuned kernels in a multi-core CPU processor and HLS implementations on FPGAs. We perform the experimental evaluation of our implementations on a low-end and a cutting-edge FPGA platform, in terms of runtime and energy consumption, and compare the results against the Intel MKL library in CPU.

We address the numerical solution of Lyapunov, algebraic and differential Riccati equations, via the matrix sign function, on platforms equipped with general-purpose multicore processors and, optionally, one or more graphics processing units (GPUs). In particular, we review the solvers for these equations, as well as the underlying methods, analyze their concurrency and scalability and provide details on their parallel implementation. Our experimental results show that this class of hardware provides sufficient computational power to tackle large-scale problems, which only a few years ago would have required a cluster of computers.

We analyze the performance-power-energy balance of a conventional Intel Xeon mul- ticore processor and two low-power architectures –an Intel Atom processor and a sys- tem with a quad-core ARM Cortex A9+NVIDIA Quadro 1000M– using a high perfor- mance implementation of Gauss-Jordan elimination (GJE) for matrix inversion. The blocked version of this algorithm employed in the experimental evaluation mostly com- prises matrix-matrix products, so that the results from the evaluation carry beyond the simple matrix inversion and are representative for a wide variety of dense linear algebra operations/codes.

RMA-11 is a numerical model widely used for studing the transport of constituents and water quality in rivers and estuaries. When applied to large water systems like the R´ıo de la Plata, RMA-11 demands long execution times to compute a simulation. This pa- per presents the analysis of the computational efficiency for the RMA-11 applied to a transport model of the R´ıo de la Plata, and introduces a proposal for improving the effi- ciency by using high performance computing techniques. The improved implementation modifies the linear system resolution methodology implemented in the model. A high performance computing strategy was applied to the FRONTALL routine of the RMA-11, by changing their logical structure and using a sparse storage format. The experimental results obtained when solving representative test cases show a significant improvement on the performance, achieving significant gains in computational speed: the execution time of the implemented version decreased up to one third of the time of the original implementation.