A Hierarchical Matrix Framework for Electromagnetics-Based Analysis and Design of Next Generation ICs

用于下一代 IC 电磁学分析和设计的分层矩阵框架

• 批准号: 0702567
• 负责人: Dan Jiao
• 金额: $ 41.5万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0702567&HistoricalAwards=false
• 关键词: Hierarchical; Matrix; Framework; Electromagnetics; Based

Proposal ID: 0702567 PI name: Dan Jiao, Venkataramanan Balakrishnan, and Chenk-Kok KohInst: Purdue UniversityTitle:A hierarchical matrix framework for electromagnetics-based analysis and design of next generation ICsABSTRACTAs IC design scales into the deep submicron and nanometer regimes, electromagnetics-based analysis has become essential. While so-called computational electromagentics (CEM) has found many successful engineering applications, the performance of existing CEM techniques is still inadequate when tackling realistic IC design problems. The analysis and design of next-generation ICs using the most accurate EM-based models results in numerical problems of very large scale, requiring up to billions of parameters to describe them accurately. However, even the state-of-art techniques do not scale well when applied to matrices of large sizes encountered with the analysis and design of next-generation ICs. In this proposal, the PIs will address the problem of full-wave analysis and design for next-generation integrated circuits, considering numerical problems arising from both partial differential equation (PDE) based models and integral equation (IE) based models. The proposed solution techniques hinge on the observation that the matrices underlying the numerical problems or their inverses are ``sparse-banded,'' wherein the matrices parametrizing the models or their inverses have (either exactly or approximately) a sparse, block-banded structure. There exists a general mathematical framework one that includes sparse-banded matrices as a special case called the ``Hierarchical Matrix'' framework, which enables a highly compact representation and efficient numerical computation. The hierarchical matrix framework will form the basis of the techniques proposed for the solution of the underlying numerical problems. The techniques combine an appreciation of the physics underlying the problems with elegant results from matrix theory and sound computational principles. This combined with the increased availability of distributed computing resources offers another rich new avenue of research. The philosophy underlying the proposed approach is that by combining advances in theory (i.e., understanding) with progress in optimization and numerical linear algebra (i.e., numerical computation), one can realize enormous advances in the state of the art in research. The PIs have considerable experience with incorporating this philosophy in their own educational efforts. The graduate students who participate in the proposed effort will be trained with a broad range of skills, in areas such as electromagnetics, numerical linear algebra, and parallel computing fundamentals. Undergraduate research projects will provide an integrated research experience to students from the sophomore through the senior years. The PIs have a history of collaboration, commitment to teaching, and fostering diversity in the workplace, and are thus well-positioned to involve a diverse population of students in the research and teaching activities envisioned in this proposal.

Proposal ID: 0702567 PI name: Dan Jiao, Venkataramanan Balakrishnan, and Chenk-Kok KohInst: Purdue UniversityTitle:A hierarchical matrix framework for electromagnetics-based analysis and design of next generation ICsABSTRACTAs IC design scales into the deep submicron and nanometer regimes, electromagnetics-based analysis has become essential. 虽然所谓的计算电动技术（CEM）发现了许多成功的工程应用，但在解决现实的IC设计问题时，现有CEM技术的性能仍然不足。 使用最准确的基于EM的模型对下一代IC的分析和设计导致非常大的数字问题，需要多达数十亿个参数才能准确描述它们。 但是，当应用于下一代IC的分析和设计时，即使是最先进的技术也无法很好地扩展。 在此提案中，考虑到基于部分微分方程（PDE）的模型和基于积分方程（IE）模型引起的数值问题，PI将解决下一代集成电路的全波分析和设计问题。提出的解决方案技术取决于观察到数值问题或其倒置的矩阵是``稀疏带式''的观察结果，其中矩阵参数化模型或其倒置具有（完全或大约）稀疏的，块状的结构。 存在一个一般的数学框架，其中包括稀疏带矩阵作为一种特殊情况，称为``层次矩阵''框架，该框架可以实现高度紧凑的表示和有效的数值计算。分层矩阵框架将构成针对基本数值问题解决方案提出的技术的基础。 这些技术结合了对问题基础物理学的欣赏以及矩阵理论和声音计算原理的优雅结果。 这与分布式计算资源的可用性增加相结合提供了另一种丰富的新研究途径。 拟议方法的基础哲学是，通过将理论的进步（即理解）与优化和数值线性代数的进步相结合（即数值计算），人们可以在研究中实现巨大进步。 PI在将这种哲学纳入自己的教育工作中具有丰富的经验。 参加拟议的工作的研究生将接受广泛的技能培训，这些技能在电磁，数值线性代数和平行计算基础上等领域。 本科研究项目将为大二学生到高年级的学生提供综合的研究经验。 PI有合作的历史，对教学的承诺以及在工作场所培养多样性的历史，因此，该提案中设想的研究和教学活动中有良好的态度。