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Efficient Solver Algorithms for Graphical Processing Units

适用于图形处理单元的高效求解器算法

基本信息

批准号：
2208470
负责人：
Eric de Sturler
金额：
$ 46.14万
依托单位：
Virginia Polytechnic Institute and State University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-08-15 至 2025-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208470&HistoricalAwards=false
关键词：
Efficient Solver Algorithms Graphical Processing

项目摘要

The extensive use of graphical processing units (GPUs) for computer simulations is transforming large-scale simulations. With algorithms that run at a good fraction of peak performance, simulations that recently were only within reach for large multinational companies and national labs are now available even to small start-up companies. Unfortunately, it is not easy to write algorithms that can exploit the peak performance of GPUs. This project focuses on linear solvers, which generally account for a very large fraction of simulation time, with the goal of improving efficiency on GPU-based architectures. More specifically, the project aims to combine a range of techniques to reduce memory usage and data movement (which is time-consuming on GPUs), better initial guesses and better stopping criteria (to halt intermediate computations earlier at an appropriate precision), and dynamic updates to solver parameters to improve efficiency. Applications targeted in this project are primarily in computational fluid dynamics, but also include inverse problems and large-scale topology optimization. The latter plays a fundamental role in the development of new micro-structure/meta materials, their use in the design of optimal structures, and their manufacturing. The project will involve a graduate research assistant and a postdoc. The project will also develop a new graduate course that combines elements of numerical linear algebra, numerical ordinary and partial differential equations, and GPU computing, all with a focus on high performance.This project involves developing iterative solvers for large-scale problems suitable for graphics processing unit (GPU) based architectures. The work aims to thoroughly reevaluate solver architecture to ensure that every part is optimized for GPUs, exposing massive fine grain parallelism in every component, maximizing throughput at every level of the GPU memory hierarchy, and minimizing data movement. This project focuses on algorithmic development that combines and analyzes three key strategies: mixed precision variants and inexact matrix-vector products and smoothers; computing better initial guesses and more effective stopping criteria and indicators; and dynamic solver optimization and flexible preconditioning strategies. The results will be tested on benchmarks developed by the Department of Energy's Center for Efficient Exascale Discretizations and similar benchmarks to be developed during this project. The theoretical underpinnings from this project will allow these solver strategies to have substantial impact beyond the immediate goals of this project. The open-source algorithms and software developed for this project will be made freely available to a wide group of potential users.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

图形处理单元（GPU）在计算机仿真中的广泛使用正在改变大规模仿真。随着算法的运行在峰值性能的很大一部分，最近只有大型跨国公司和国家实验室才能实现的模拟现在甚至可以用于小型初创公司。不幸的是，编写可以利用GPU峰值性能的算法并不容易。该项目的重点是线性求解器，通常占仿真时间的很大一部分，目标是提高基于GPU的架构的效率。更具体地说，该项目旨在联合收割机结合一系列技术来减少内存使用和数据移动（这在GPU上很耗时），更好的初始猜测和更好的停止标准（以适当的精度提前停止中间计算），以及动态更新求解器参数以提高效率。在这个项目中的应用目标主要是在计算流体动力学，但也包括逆问题和大规模拓扑优化。后者在新的微结构/Meta材料的开发，它们在最佳结构设计中的应用以及它们的制造中起着重要作用。该项目将涉及一名研究生助理和一名博士后。该项目还将开发一个新的研究生课程，结合数值线性代数，数值常微分方程和偏微分方程，以及GPU计算的元素，所有这些都以高性能为重点。该项目涉及开发适用于基于图形处理器（GPU）架构的大规模问题的迭代求解器。这项工作旨在彻底重新评估求解器架构，以确保每个部分都针对GPU进行了优化，在每个组件中暴露大量细粒度并行性，最大限度地提高GPU内存层次结构每个级别的吞吐量，并最大限度地减少数据移动。该项目的重点是算法开发，结合和分析三个关键策略：混合精度变量和不精确的矩阵向量乘积和平滑器;计算更好的初始猜测和更有效的停止标准和指标;动态求解器优化和灵活的预处理策略。结果将在能源部高效Exascale离散化中心开发的基准测试和该项目期间开发的类似基准测试上进行测试。该项目的理论基础将使这些求解器策略产生超出该项目直接目标的实质性影响。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。