| Research Abstract |
In this project, we first propose a new algorithm using the fixed-point homotopy that is globally convergent for modified nodal equations. Using this algorithm, bipolar analog integrated circuits with more than 15,000 elements are solved efficiently. We prove a theorem that guarantees the global convergence of the proposed algorithm under mild conditions. We also show that the proposed algorithm converges to a stable operating point with high possibility.
We next proposed an efficient algorithm for finding all solutions of piecewise-linear resistive circuits using linear programming. Using this algorithm, all solutions of large scale problems, including those where the number of variables is 300 and the number of linear regions is 10^<300>, could be solved in practical computation time.
We also studied the problem of calculating multiphase equilibria of polymer solutions, which is a very difficult problem in polymer chemistry. We discovered an interesting phenomena termed the reentrant three-phase equilibria of polymer solutions, and exploiting this phenomena, we calculated four-phase equilibria of polymer solutions for the first time.
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