AF: Small: Metanumerical Computing for Emerging Architectures: Automated Embedded Algorithms for Partial Differential Equations on Multicore Platforms

AF：小型：新兴架构的元数值计算：多核平台上偏微分方程的自动化嵌入式算法

• 批准号: 1117794
• 负责人: Robert Kirby
• 金额: $ 49.97万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-10-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1117794&HistoricalAwards=false
• 关键词: AF; Small; Metanumerical; Computing; Emerging

Computers were invented to automate tedious and error-pronetasks, especially in the context of numerical calculations forscientific simulation. Given the importance and difficulty of developing these simulations, it makes sense to study whether computers can assist in their production as well. This project focuses on the open-source project Sundance, which provideshigh-level syntax to describe finite element methods (FEM) for thenumerical solution of partial differential equations, freeing users from the burdens of low-level programming. This approach can reduce development time from months to days or even hours, allowing scientists and engineers to get correct answers more quickly. Sundance is useful software starting from a solid theoretical basis,where the structure of finite element operators are derived andanalyzed from software-based Frechet differentiation of variationalforms.Via this domain-specific embedded language, Sundance users (domainscientistis and engineers) can express and simulate nonlinear processes with little more difficulty than linear ones; Jacobians are calculated internally and automatically. This robust system automates not only standard simulations, but also sensitivity calculations, eigenvalueproblems, and PDE-constrained optimization, all through the language ofdifferentiation, providing a simple gateway to efficient ``embedded''algorithms for optimization and control. Furthermore, in this project, Sundance will be extended to run on emerging architectures such as multicore CPU and GPU machines. New low-complexity finite element algorithms based on Bernstein polynomials will be developed and included within Sundance to further exploit this new hardware. Thus, this project represents concrete transformational contributions not only automatingmathematical software but in core numerical algorithms, broadening thecircle of domain specialists with access to leading-edge simulationtechnology.

发明计算机是为了使繁琐和容易出错的任务自动化，特别是在科学模拟的数值计算中。考虑到开发这些模拟的重要性和难度，研究计算机是否也能辅助它们的制作是有意义的。这个项目的重点是开源项目Sundance，它提供了用于描述偏微分方程数值解的有限元方法（FEM）的高级语法，将用户从低级编程的负担中解放出来。这种方法可以将开发时间从几个月缩短到几天甚至几个小时，使科学家和工程师能够更快地得到正确的答案。Sundance是一个有用的软件，从坚实的理论基础开始，其中有限元算子的结构是从基于软件的变分形式的Frechet微分中导出和分析的。通过这种特定于领域的嵌入式语言，Sundance用户（领域科学家和工程师）可以比线性过程更容易地表达和模拟非线性过程；雅可比矩阵是内部自动计算的。这个强大的系统不仅可以自动化标准模拟，还可以通过微分语言自动化灵敏度计算，特征值问题和pde约束优化，为高效的“嵌入式”优化和控制算法提供了一个简单的门户。此外，在这个项目中，Sundance将扩展到运行在新兴架构上，如多核CPU和GPU机器。新的基于Bernstein多项式的低复杂度有限元算法将被开发并包含在Sundance中，以进一步利用这种新的硬件。因此，该项目不仅代表了自动化数学软件，而且代表了核心数值算法的具体变革贡献，扩大了领域专家的圈子，获得了领先的仿真技术。