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

提案ID：0702567 PI名称：Dan Jiao，Venkataramanan Balakrishnan和Chenk-Kok KohInst：普渡大学标题：基于电磁学的下一代IC分析和设计的分层矩阵框架摘要随着IC设计进入深亚微米和纳米区域，基于电磁学的分析已变得必不可少。虽然所谓的计算电磁学(CEM)已经在工程上得到了许多成功的应用，但现有的CEM技术在解决实际IC设计问题时仍然存在不足。使用最精确的基于EM的模型分析和设计下一代IC会导致非常大规模的数值问题，需要高达数十亿个参数才能准确地描述它们。然而，即使是最先进的技术，在应用于分析和设计下一代IC时遇到的大尺寸矩阵时，也不能很好地扩展。在这项建议中，PI将解决下一代集成电路的全波分析和设计问题，同时考虑基于偏微分方程(PDE)的模型和基于积分方程(IE)的模型所产生的数值问题。所提出的解决技术取决于这样的观察，即作为数值问题或其逆的基础的矩阵是“稀疏带状”的，其中将模型或其逆参数化的矩阵具有(精确地或近似地)稀疏的块带状结构。有一个通用的数学框架，其中包括作为特殊情况的稀疏带状矩阵，称为“层次矩阵”框架，它使高度紧凑的表示和有效的数值计算成为可能。分层矩阵框架将构成为解决基本数值问题而提出的技术的基础。这些技术将对潜在问题的物理学的欣赏与来自矩阵理论的优雅结果和合理的计算原理结合在一起。这一点，再加上分布式计算资源可用性的提高，提供了另一条丰富的新研究途径。提出的方法背后的哲学是，通过将理论的进步(即理解)与最优化和数值线性代数的进步(即数值计算)相结合，可以实现研究最新水平的巨大进步。在将这一理念融入他们自己的教育工作方面，私人投资机构拥有相当丰富的经验。参与这项计划的研究生将在电磁学、数值线性代数和并行计算基础等领域接受广泛的技能培训。本科生研究项目将为从大二到大四的学生提供综合研究体验。私人投资机构具有合作、致力于教学和促进工作场所多样性的历史，因此处于有利地位，可以让不同群体的学生参与本提案所设想的研究和教学活动。

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.