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Register a new userScalability of High-Performance PDE Solvers
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Added by
Misun Min Dr
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Performance tests and analyses are critical to effective HPC software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this paper, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for PDEs that govern a wide range of physical applications. We consider a sequence of PDE- motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.
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The life-cycle of a partial differential equation (PDE) solver is often characterized by three development phases: the development of a stable numerical discretization, development of a correct (verified) implementation, and the optimization of the implementation for different computer architectures. Often it is only after significant time and effort has been invested that the performance bottlenecks of a PDE solver are fully understood, and the precise details varies between different computer architectures. One way to mitigate this issue is to establish a reliable performance model that allows a numerical analyst to make reliable predictions of how well a numerical method would perform on a given computer architecture, before embarking upon potentially long and expensive implementation and optimization phases. The availability of a reliable performance model also saves developer effort as it both informs the developer on what kind of optimisations are beneficial, and when the maximum expected performance has been reached and optimisation work should stop. We show how discretization of a wave equation can be theoretically studied to understand the performance limitations of the method on modern computer architectures. We focus on the roofline model, now broadly used in the high-performance computing community, which considers the achievable performance in terms of the peak memory bandwidth and peak floating point performance of a computer with respect to algorithmic choices. A first principles analysis of operational intensity for key time-stepping finite-difference algorithms is presented. With this information available at the time of algorithm design, the expected performance on target computer systems can be used as a driver for algorithm design.
CUDA and OpenCL are two different frameworks for GPU programming. OpenCL is an open standard that can be used to program CPUs, GPUs, and other devices from different vendors, while CUDA is specific to NVIDIA GPUs. Although OpenCL promises a portable language for GPU programming, its generality may entail a performance penalty. In this paper, we use complex, near-identical kernels from a Quantum Monte Carlo application to compare the performance of CUDA and OpenCL. We show that when using NVIDIA compiler tools, converting a CUDA kernel to an OpenCL kernel involves minimal modifications. Making such a kernel compile with ATIs build tools involves more modifications. Our performance tests measure and compare data transfer times to and from the GPU, kernel execution times, and end-to-end application execution times for both CUDA and OpenCL.
Cloud computing has become increasingly popular. Many options of cloud deployments are available. Testing cloud performance would enable us to choose a cloud deployment based on the requirements. In this paper, we present an innovative process, implemented in software, to allow us to assess the quality of the cloud performance data. The process combines performance data from multiple machines, spanning across user experience data, workload performance metrics, and readily available system performance data. Furthermore, we discuss the major challenges of bringing raw data into tidy data formats in order to enable subsequent analysis, and describe how our process has several layers of assessment to validate the quality of the data processing procedure. We present a case study to demonstrate the effectiveness of our proposed process, and conclude our paper with several future research directions worth investigating.
This work examines the performance of leading-edge systems designed for machine learning computing, including the NVIDIA DGX-2, Amazon Web Services (AWS) P3, IBM Power System Accelerated Compute Server AC922, and a consumer-grade Exxact TensorEX TS4 GPU server. Representative deep learning workloads from the fields of computer vision and natural language processing are the focus of the analysis. Performance analysis is performed along with a number of important dimensions. Performance of the communication interconnects and large and high-throughput deep learning models are considered. Different potential use models for the systems as standalone and in the cloud also are examined. The effect of various optimization of the deep learning models and system configurations is included in the analysis.
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