Research on GlobalAlgorithms for Solving Large-Scale Integrated Circuits and Their Applications

在这个项目中，我们首次提出了求解大规模集成电路的高效同伦方法，并从理论上保证了算法的全局收敛。特别是，我们提出了变增益牛顿同伦方法，这似乎是最有效的同伦方法。在此基础上，提出了一种无需编程即可在SPICE上实现同伦方法的有效方法。这些研究的论文发表在IEEE电路与系统学报等国际期刊上，然后提出了寻找非线性电阻电路所有解的有效算法，并首次在实际计算时间内成功地找到了大规模的非线性电路。这些研究的论文发表在国际期刊上，如位数字数学，国际电路理论和应用杂志，电路，系统和计算机杂志等。其中一项研究获得了IEEE ICC…最佳论文奖更多CAS 2007。其中一些研究被提交给国际会议，如第15届IEEE NDE应邀演讲。我们还提出了各种方法，使用面向SPICE的方法。这种方法使SPICE适用于更广泛的科学问题，如数学规划问题，也使同伦方法易于在SPICE上实现而不需要特殊知识。这些研究的论文发表在许多国际期刊上，其中一些论文还应邀在WEE NCN 2007和第17届RAMP研讨会等国际会议上发表，我们进一步提出了一种利用集值函数概念进行非线性电路容差分析的有效方法，并表明该方法大大提高了电路设计的可靠性。这些研究的论文发表在《电路、系统和计算机杂志》等国际期刊上。

In this project, we first proposed efficient homotopy methods for solving large-scale integrated circuits with the theoretical guarantee of global convergence. Especially, we proposed the variable gain Newton homotopy method, which seems to be the most efficient homotopy methods. We further proposed an effective method for implementing the homotopy methods on SPICE easily without programming. The papers of these studies were published in international journals such as IEEE Transactions on Circuits and Systems, etc.We next proposed efficient algorithms for finding all solutions of nonlinear resistive circuits, and succeeded in finding large scale nonlinear circuits in practical computation time for the first time. The papers of these studies were published in international journals such as BIT-Numerical Mathematics-, International Journal of Circuit Theory and Applications, Journal of Circuits, Systems, and Computers, etc. One of the studies received the Best Paper Award of the IEEE ICC … More CAS 2007. Some of the studies were presented in international conferences such as 15th IEEE NDES as Invited Talks.We also proposed various methods using the SPICE-oriented approach. Using this approach, numerical analysis without programming is possible, and various techniques implemented in SPICE make the numerical analysis very efficient This approach makes SPICE applicable to a broader class of scientifir problems such as mathematiral programming problems, arid also makes the homotopy methods easily implemented on SPICE without special knowledge. The papers of these studies were published in many international journals, and some of them were presented in international conferences such as WEE NCN 2007 and the 17th RAMP Symposium as Invited Talks.We further proposed an efficient method for the tolerance analysis of nonlinear circuits using the concept of set-valued functions, and showed that this method improves the reliability of circuit design substantially. The papers of these studies were published in international journals such as Journal of Circuits, Systems, and Computers, etc. Less