179 research outputs found
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Preparing sparse solvers for exascale computing.
Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'
Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects
We first briefly report on the status and recent achievements of the ELPA-AEO
(Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and
Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects.
In both collaboratory efforts, scientists from the application areas,
mathematicians, and computer scientists work together to develop and make
available efficient highly parallel methods for the solution of eigenvalue
problems. Then we focus on a topic addressed in both projects, the use of mixed
precision computations to enhance efficiency. We give a more detailed
description of our approaches for benefiting from either lower or higher
precision in three selected contexts and of the results thus obtained
GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis
Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs
GPU-Resident Sparse Direct Linear Solvers for Alternating Current Optimal Power Flow Analysis
Integrating renewable resources within the transmission grid at a wide scale
poses significant challenges for economic dispatch as it requires analysis with
more optimization parameters, constraints, and sources of uncertainty. This
motivates the investigation of more efficient computational methods, especially
those for solving the underlying linear systems, which typically take more than
half of the overall computation time. In this paper, we present our work on
sparse linear solvers that take advantage of hardware accelerators, such as
graphical processing units (GPUs), and improve the overall performance when
used within economic dispatch computations. We treat the problems as sparse,
which allows for faster execution but also makes the implementation of
numerical methods more challenging. We present the first GPU-native sparse
direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate
significant performance improvements when using high-performance linear solvers
within alternating current optimal power flow (ACOPF) analysis. Furthermore, we
demonstrate the feasibility of getting significant performance improvements by
executing the entire computation on GPU-based hardware. Finally, we identify
outstanding research issues and opportunities for even better utilization of
heterogeneous systems, including those equipped with GPUs
Linear solvers for power grid optimization problems: a review of GPU-accelerated linear solvers
The linear equations that arise in interior methods for constrained
optimization are sparse symmetric indefinite and become extremely
ill-conditioned as the interior method converges. These linear systems present
a challenge for existing solver frameworks based on sparse LU or LDL^T
decompositions. We benchmark five well known direct linear solver packages
using matrices extracted from power grid optimization problems. The achieved
solution accuracy varies greatly among the packages. None of the tested
packages delivers significant GPU acceleration for our test cases
Development and performance of a HemeLB GPU code for human-scale blood flow simulation
In recent years, it has become increasingly common for high performance computers (HPC) to possess some level of heterogeneous architecture - typically in the form of GPU accelerators. In some machines these are isolated within a dedicated partition, whilst in others they are integral to all compute nodes - often with multiple GPUs per node - and provide the majority of a machine's compute performance. In light of this trend, it is becoming essential that codes deployed on HPC are updated to execute on accelerator hardware. In this paper we introduce a GPU implementation of the 3D blood flow simulation code HemeLB that has been developed using CUDA C++. We demonstrate how taking advantage of NVIDIA GPU hardware can achieve significant performance improvements compared to the equivalent CPU only code on which it has been built whilst retaining the excellent strong scaling characteristics that have been repeatedly demonstrated by the CPU version. With HPC positioned on the brink of the exascale era, we use HemeLB as a motivation to provide a discussion on some of the challenges that many users will face when deploying their own applications on upcoming exascale machines
LFRic: meeting the challenges of scalability and performance portability in weather and climate models
This paper describes LFRic: the new weather and climate modelling
system being developed by the UK Met Office to replace the existing
Unified Model in preparation for exascale computing in the 2020s.
LFRic uses the GungHo dynamical core and runs on a semi-structured
cubed-sphere mesh. The design of the supporting infrastructure follows
object-oriented principles to facilitate modularity and the use of
external libraries where possible. In particular, a `separation of concerns'
between the science code and parallel code is imposed to promote
performance portability. An application called PSyclone, developed at the
STFC Hartree centre, can generate the parallel code enabling deployment of
a single source science code onto different machine architectures.
This paper provides an overview of the scientific requirement, the design
of the software infrastructure, and examples of PSyclone usage. Preliminary
performance results show strong scaling and an indication that hybrid
MPI/OpenMP performs better than pure MPI
Software for Exascale Computing - SPPEXA 2016-2019
This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest
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