Energy‐aware strategies for task‐parallel sparse linear system solvers

This is the pre-peer reviewed version of the following article: Energy‐aware strategies for task‐parallel sparse linear system solvers, which has been published in final form at https://doi.org/10.1002/cpe.4633. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.We present several energy‐aware strategies to improve the energy efficiency of a task‐parallel preconditioned Conjugate Gradient (PCG) iterative solver on a Haswell‐EP Intel Xeon. These techniques leverage the power‐saving states of the processor, promoting the hardware into a more energy‐efficient C‐state and modifying the CPU frequency (P‐states of the processors) of some operations of the PCG. We demonstrate that the application of these strategies during the main operations of the iterative solver can reduce its energy consumption considerably, especially for memory‐bound computations

GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems

While many of the architectural details of future exascale-class high performance computer systems are still a matter of intense research, there appears to be a general consensus that they will be strongly heterogeneous, featuring "standard" as well as "accelerated" resources. Today, such resources are available as multicore processors, graphics processing units (GPUs), and other accelerators such as the Intel Xeon Phi. Any software infrastructure that claims usefulness for such environments must be able to meet their inherent challenges: massive multi-level parallelism, topology, asynchronicity, and abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a collection of building blocks that targets algorithms dealing with sparse matrix representations on current and future large-scale systems. It implements the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel numerical kernels, intelligent resource management, and truly heterogeneous parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We describe the details of its design with respect to the challenges posed by modern heterogeneous supercomputers and recent algorithmic developments. Implementation details which are indispensable for achieving high efficiency are pointed out and their necessity is justified by performance measurements or predictions based on performance models. The library code and several applications are available as open source. We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrates the applicability and performance of GHOST as a component within a larger software stack.Comment: 32 pages, 11 figure

Enhancing Energy Production with Exascale HPC Methods

High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imagingPostprint (author's final draft

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Resiliency in numerical algorithm design for extreme scale simulations

This work is based on the seminar titled ‘Resiliency in Numerical Algorithm Design for Extreme Scale Simulations’ held March 1–6, 2020, at Schloss Dagstuhl, that was attended by all the authors. Advanced supercomputing is characterized by very high computation speeds at the cost of involving an enormous amount of resources and costs. A typical large-scale computation running for 48 h on a system consuming 20 MW, as predicted for exascale systems, would consume a million kWh, corresponding to about 100k Euro in energy cost for executing 1023 floating-point operations. It is clearly unacceptable to lose the whole computation if any of the several million parallel processes fails during the execution. Moreover, if a single operation suffers from a bit-flip error, should the whole computation be declared invalid? What about the notion of reproducibility itself: should this core paradigm of science be revised and refined for results that are obtained by large-scale simulation? Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? While the analysis of use cases can help understand the particular reliability requirements, the construction of remedies is currently wide open. One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. These ideas constituted an essential topic of the seminar. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge. This article gathers a broad range of perspectives on the role of algorithms, applications and systems in achieving resilience for extreme scale simulations. The ultimate goal is to spark novel ideas and encourage the development of concrete solutions for achieving such resilience holistically.Peer Reviewed"Article signat per 36 autors/es: Emmanuel Agullo, Mirco Altenbernd, Hartwig Anzt, Leonardo Bautista-Gomez, Tommaso Benacchio, Luca Bonaventura, Hans-Joachim Bungartz, Sanjay Chatterjee, Florina M. Ciorba, Nathan DeBardeleben, Daniel Drzisga, Sebastian Eibl, Christian Engelmann, Wilfried N. Gansterer, Luc Giraud, Dominik G ̈oddeke, Marco Heisig, Fabienne Jezequel, Nils Kohl, Xiaoye Sherry Li, Romain Lion, Miriam Mehl, Paul Mycek, Michael Obersteiner, Enrique S. Quintana-Ortiz, Francesco Rizzi, Ulrich Rude, Martin Schulz, Fred Fung, Robert Speck, Linda Stals, Keita Teranishi, Samuel Thibault, Dominik Thonnes, Andreas Wagner and Barbara Wohlmuth"Postprint (author's final draft

Model Reduction of Synchronized Lur'e Networks

In this talk, we investigate a model order reduction schemethat reduces the complexity of uncertain dynamical networks consisting of diffusively interconnected nonlinearLure subsystems. We aim to reduce the dimension ofeach subsystem and meanwhile preserve the synchronization property of the overall network. Using the upperbound of the Laplacian spectral radius, we first characterize the robust synchronization of the Lure network bya linear matrix equation (LMI), whose solutions can betreated as generalized Gramians of each subsystem, andthus the balanced truncation can be performed on the linear component of each Lure subsystem. As a result, thedimension of the each subsystem is reduced, and the dynamics of the network is simplified. It is verified that, withthe same communication topology, the resulting reducednetwork system is still robustly synchronized, and the apriori bound on the approximation error is guaranteed tocompare the behaviors of the full-order and reduced-orderLure subsyste