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

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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