Advanced Computational Electromagnetism -- ACE '06 Workshop

高级计算电磁学 -- ACE 06 研讨会

• 批准号: 0606622
• 负责人: P. Robert Kotiuga
• 金额: $ 2.5万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-04-01 至 2007-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0606622&HistoricalAwards=false
• 关键词: Advanced; Computational; Electromagnetism; ACE; 06

The Whitney form revolution in computational electromagnetics, initiated over two decades ago, builds on the mathematics which created discrete Hodge theory, solved the Ray-Singer conjecture and set the stage for Dennis Sullivan's approach to rational homotopy theory. The basic tools point to a discrete framework for Ed Witten's TQFT approach to the Jones polynomial, and associated computational complexity issues. Furthermore, this interaction between electrical engineers and geometrically minded topologists was largely unnoticed by applied mathematicians! ACE '06 will bring together experts in very diverse fields to continue this technology transfer from seemingly pure mathematics to deep problems encountered in enlarging the scope of computational electromagnetics.Electrical engineers have always marveled at the beauty of Maxwell's theory of electromagnetism and associated mathematical formalism. They have pondered both the practical implications of this big picture, and the difficulties of fitting it into the undergraduate curriculum. The Whitney form revolution of the past two decades has translated the formalism associated with Mawell's equations into a discrete setting, has resolved some of the deepest problems in computational electromagnetics, has lead to very efficient software implementations, has enabled unforeseen applications to be tackled, and has offered open research questions back to mathematicians. A major objective in organizing this workshop is to get key mathematicians who have been cited by engineers years ago, to finally rub shoulders with the key players within the engineering community! By having a diverse set talks, poster sessions, and panel discussions, ACE '06 will sustain the strong level of cross-fertilization by bringing from different countries, a diverse set of experts and academic disciplines, students, professors, and engineers who have grown successful companies. More information can be found on the conference webpage:http://www.bu.edu/eng/ace2006/

计算电磁学中的惠特尼形式革命始于二十多年前，建立在创建离散霍奇理论的数学基础上，解决了雷-辛格猜想，并为丹尼斯·沙利文的理性同伦理论方法奠定了基础。基本的工具指向一个离散的框架艾德维滕的TQFT方法的琼斯多项式，和相关的计算复杂性问题。此外，电气工程师和具有几何头脑的拓扑学家之间的这种相互作用在很大程度上没有被应用数学家注意到！ACE '06将汇集非常不同领域的专家，继续这种技术转移，从表面上纯数学的深层问题，在扩大范围的计算电磁学。电气工程师一直惊叹于美丽的麦克斯韦的电磁理论和相关的数学形式主义。他们思考了这一大图景的实际含义，以及将其融入本科课程的困难。过去二十年的惠特尼形式革命已经将与Mawell方程相关的形式主义转化为离散设置，解决了计算电磁学中一些最深刻的问题，导致了非常有效的软件实现，使不可预见的应用得以解决，并为数学家提供了开放的研究问题。组织这次研讨会的一个主要目标是让几年前被工程师引用的关键数学家最终与工程界的关键人物接触！ACE '06将通过举办多样化的演讲、海报展示和小组讨论，吸引来自不同国家的专家和学术学科、学生、教授和成功公司的工程师，保持强大的交流水平。更多信息可以在会议网页上找到：http://www.bu.edu/eng/ace2006/