Computing with sparse and structured matrices: mathematical derivatives and beyond

使用稀疏矩阵和结构化矩阵进行计算：数学导数及其他

• 批准号: 228155-2009
• 负责人: Hossain, Shahadat
• 金额: $ 1.38万
• 依托单位: University of Lethbridge
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503358
• 关键词: Computing; sparse; structured; matrices; mathematical

One of the central themes of my current research is the synergy of combinatorics, graph theory, and numerical linear algebra to explore new and innovative ways of formulating and solving important scientific problems. With the technological advances in high performance computing systems a major challenge confronted by researchers is concerned with the design of effective algorithmic tools and frameworks that exploit the problem structure and the computing system architecture to solve increasingly complex and extremely large scientific problems. Accurate climate modeling code such as ``Community Climate System Model'', for example, belongs to the so called ``petascale simulation'' applications. One of the necessary computational components of such a simulation model is concerned with the efficient calculation of ``sensitivities'' of a large number of output parameters with respect to a small subset of model inputs. Exploiting a priori known information such as sparsity and structure of the underlying problem is crucial for designing effective algorithms for such applications. Additionally, the architectural complexity of modern high performance computing systems pose considerable

我目前研究的中心主题之一是组合学、图论和数值线性代数的协同作用，以探索阐明和解决重要科学问题的新的和创新的方法。随着高性能计算系统的技术进步，研究人员面临的一个主要挑战是如何设计有效的算法工具和框架，利用问题结构和计算系统体系结构来解决日益复杂和极其庞大的科学问题。精确的气候建模代码，如“社区气候系统模型”，就属于所谓的“千万亿级模拟”应用。这种模拟模型的必要计算组成部分之一是有效地计算大量输出参数相对于模型输入的一小部分的“敏感性”。利用先验已知的信息，如稀疏性和潜在问题的结构，对于为此类应用设计有效的算法至关重要。此外，现代高性能计算系统的体系结构复杂性也提出了相当大的要求