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

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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