CAREER: From O(N) to O(M): Scalable Algorithms for Large Scale Electromagnetics-Based Analysis and Design of Next Generation VLSI Circuits

综合、混合与复杂系统杜克大学dan娇职业：从O(N)到O(M)：大规模电磁分析与下一代VLSI电路设计的可扩展算法随着片上设计规模扩展到纳米级，由于亚波长光刻的特征尺寸减小、时钟频率增加、从单核到多核的过渡以及集成水平的提高，全波电磁学（EM）分析变得越来越重要。然而，下一代集成电路的设计会导致非常大规模的数值问题，需要数十亿个参数才能准确描述。最先进的EM分析算法需要与N（未知数）成比例的计算和内存。本研究的重点是降低所需计算和内存的复杂性，使其与M（设计决策参数的数量）成比例，M是一个远小于未知量的值。这种复杂性的降低是实现下一代超大规模集成（VLSI）电路的EM分析所必需的。我们不再求解O(N)的原始矩阵，而是构建了一个简化矩阵，该矩阵只涉及电路设计决策所需的O(M)个参数，同时考虑了其他参数的影响。此外，原始的和简化的系统矩阵具有或可以被表述为具有特殊的结构，例如稀疏带状结构。在半可分离矩阵的框架下，探索或创造结构以降低约简和解约简系统矩阵的复杂性。更广泛的影响：该项目的教育目标是有效地将领域教育与电路教育联系起来，并有效地将人的维度引入集成电路领域教育。将开发三个教育项目：(i)“电路和领域”的本科课程，（ii）“高频计算机辅助设计工作室”的研究生课程，以及（iii）“工作与差异学习社区”。评估任务将评估这些计划的有效性。本研究有潜力为解决集成电路设计中现有计算EM技术的可扩展性问题做出重大贡献。此外，它还具有广泛的工程应用潜力，在这些应用中，大问题规模是阻碍先进系统成功设计和分析的瓶颈

Integrative, Hybrid and Complex SystemsPurdue UniversityDan JiaoCAREER: From O(N) to O(M): Scalable Algorithms for Large Scale Electromagnetics-Based Analysis and Design of Next Generation VLSI CircuitsIntellectual Merit: As on-chip design scales into the nanometer regime, full-wave electromagnetics (EM) analysis has increasingly become essential due to reduced feature sizes that lead to subwavelength optical lithography, increased clock frequency, the transition from single core to multicore, and increased levels of integration. However, the design of next-generation integrated circuits results in numerical problems of very large scale, requiring billions of parameters to describe accurately. State-of-the-art EM analysis algorithms require computation and memory that scales with N, the number of unknowns. This research focuses on reducing the complexity of required computation and memory to scale with M, the number of design decision parameters, which is a much smaller value than the number of unknowns. This reduction in complexity is required to enable the EM analysis of next-generation very large-scale integrated (VLSI) circuits. Instead of solving the original matrix of O(N) as it is, we construct a reduced matrix that involves only the O(M) parameters needed for the circuit design decision, while incorporating the effects of other parameters. Moreover, the original and reduced system matrices possess, or can be formulated to possess, special structure, for example a sparse banded structure. The structure will be explored or created to reduce the complexity of the reduction and the solution of the reduced system matrix under the framework of semi-separable matrices.Broader Impact: The project's education objectives are to effectively bridge the education in fields with that in circuits and to effectively introduce the human dimension into the integrated circuit-field education. Three education programs will be developed: (i) an undergraduate course in "Circuits and Fields," (ii) a graduate "High-Frequency Computer-Aided Design Studio," and (iii) a "Working-with-Differences Learning Community." Assessment tasks will evaluate the effectiveness of these programs. This research has the potential to contribute significantly to solving scalability problems with existing computational EM techniques for integrated circuit design. In addition, it has the potential to benefit a wide range of engineering applications in which large problem sizes are a bottleneck in preventing the successful design and analysis of advanced system