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求解器、优化技术和统计建模中。计算机硬件的创新，如多核处理器和可扩展多处理器，提供了巨大的性能潜力，同时对高效求解器的设计提出了重大挑战。该项目在名为Spike的新型强大解算器的背景下解决了这些挑战。Spike将一个线性系统分解为一组解耦系统，以及一个更小的简化系统。这种新颖的分解导致内存引用和处理器间通信的水平大大降低，代价是算术运算的数量适度增加。该项目研究了Spike的基本数值、算法和软件开发方面。它解决了矩阵重新排序、存储方案、底层直接和迭代求解器、错误分析和全面验证。它通过最小化内存引用和最大化并发性，直接关注新兴硬件平台。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业用户提供最有效的Spike版本。该项目还将Spike集成到最先进的量子尺度纳米电子学模拟环境NESSIE中，以展示真正的应用性能。Spike工具包是一个通用软件包，可用于各种科学计算应用程序。这种求解器的广泛影响是巨大的，它非常适合新兴平台。通过将Spike集成到NESSIE中，该项目对量子尺度建模环境具有重要影响。该项目通过开发新颖的教学材料、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.