Small: Collaborative Research: Transform-to-Perform: Languages, Algorithms, and Code Transformations for High-Performance FEM

自然和工程现象的模拟是一项多层次的技术任务，对数学复杂度和计算能力有很高的要求。制作计算机模拟代码需要在许多不同的细节级别上进行工作。计算机程序应该用一种接近领域专家使用的语言来表示科学问题，但这与计算机的低级、特定于硬件的细节有很大的不同。两者之间的桥梁需要几个不同的链接。这个项目建立了许多中间软件阶段，称为？表示？通过描述偏微分方程、数值方法所需的所谓弱形式、构建离散运算所需的循环嵌套以及计算机可执行的低级代码，对工程师、数值分析师和计算机科学家的领域知识进行建模。？转变？然后是连接这些表示的程序，注入关于算法和硬件的知识。这项研究的关键进展是，通过这种转换链，可以在适当的详细级别提供关于每个细节级别的领域知识，无论是与应用程序相关的、数值的还是计算的。该项目开发的工具既缩短了开发时间，又增加了科学家和工程师使用的高性能模拟代码的结果能力，使它们能够影响世界，从而促进了科学的进步。

Simulation of natural and engineering phenomena is a multi-layered technical task with high demands on mathematical sophistication and computational power. Producing a computer simulation code requires work at many different levels of detail. A computer program should represent a scientific problem in a language close to that used by domain specialists, but this differs greatly from low-level, hardware-specific details of computers. Bridging between the two requires several different links. This project sets up many intermediate software stages, called ?representations? modeling the domain knowledge of engineers, numerical analysts, and computer scientists by describing partial differential equations, the so-called weak forms needed for numerical methods, loop nests required to build discrete operations, and finally low-level code that can be executed by computers. ?Transformations? are then programs connecting these representations, injecting knowledge about algorithms and hardware. The key advance in this research is that, through this chain of transformations, domain knowledge about each level of detail, be it application-related, numerical, or computational, can be supplied at the appropriate level of detail. The tools developed in this project promote the advancement of science by both shortening the development time and increasing the resulting power of high-performance simulation codes used by scientists and engineers, enabling them to impact the world.