Collaborative Research: Developing A Robust Parallel Hybrid System Solver

稀疏线性系统解算器是一大类科学和工程应用的核心。它们出现在偏微分方程解程序、优化技术和统计建模中。计算机硬件的创新，如多核处理器和可伸缩多处理器，提供了巨大的性能潜力，同时也给高效求解器的设计带来了巨大的挑战。这个项目在一个名为Spike的新的、功能强大的求解器的背景下解决了这些挑战。Spike将一个线性系统分解成一组解耦的系统，以及一个小得多的简化系统。这种新颖的分解导致内存引用和处理器间通信的级别大大减少，但代价是算术运算的数量略有增加。本项目研究了Spike的基本数值、算法和软件开发方面。它涉及矩阵重新排序、存储方案、底层直接和迭代求解器、误差分析和综合验证。它通过最小化内存引用和最大化并发性，直接专注于新兴硬件平台。该项目还旨在创建一个工具包，可以根据底层硬件特征自动为非专家用户提供最高效的Spike版本。该项目还将Spike集成到最先进的量子规模纳米电子模拟环境Nessie中，以演示真正的应用性能。Spike工具包是一种通用软件包，可用于各种科学计算应用程序。这样的解算器非常适合新兴平台，其更广泛的影响是巨大的。通过将Spike集成到Nessie中，该项目对量子规模的建模环境产生了重大影响。该项目通过开发新的教学材料、新课程、课堂项目和软件，在教育和推广方面做出了重大贡献。

Sparse linear system solvers are at the heart of a large class of science and engineering applications. They arise in partial differential equation solvers, optimization techniques, and statistical modeling. Innovations in computer hardware, such as multicore processors and scalable multiprocessors offer tremendous performance potential, while posing significant challenges for the design of efficient solvers. This project addresses these challenges in the context of a new and powerful solver called Spike. Spike decomposes a linear system into a set of decoupled systems, and a much smaller reduced system. Such a novel decomposition results in a much reduced level of memory references and interprocessor communications, at the cost of a modest increase in the number of arithmetic operations.This project investigates fundamental numerical, algorithmic, and software development aspects of Spike. It addresses matrix reordering, storage schemes, underlying direct and iterative solvers, error analysis, and comprehensive validation. It directly focuses on emerging hardware platforms by minimizing memory references and maximizing concurrency. The project also aims to create a toolkit that can automatically provide a non-expert user with the most efficient version of Spike, based on the underlying hardware characteristics. The project also integrates Spike into a state-of-the-art quantum-scale nanoelectronics simulation environment, NESSIE, to demonstrate true application performance. The Spike toolkit is a general-purpose software package useful in a wide variety of scientific computing applications. The broader impact of such a solver, which is well well-suited to emerging platforms, is tremendous. By integrating Spike into NESSIE, this project has significant impact on quantum-scale modeling environments. The project makes significant educational and outreach contributions through the development of novel instructional material, new courses, classroom projects, and software.