在通信产业和智能终端等应用的发展中，模拟电路仿真技术至关重要，它是保障集成电路芯片和电子产品设计、测试、诊断、维护全寿命周期可靠性的重要手段。在电路仿真中，直流分析不仅是电路运行的基本评定，还是其他分析方法如交流、暂态分析的必要基础，因此对直流分析的研究具有重要的理论和实际意义。本项目针对现有仿真算法的技术瓶颈，以进一步提高大规模电路直流分析的收敛性和收敛效率为目标，以伪暂态法和同伦法为切入点，着重研究如下内容：（1）提出一种带强阻尼和步长优化控制的纯伪瞬态法，解决振荡、解曲线不连续和步长设置不当的问题，提高大规模电路的收敛性和收敛效率；（2）提出一种基于解耦合思想和非奇异降维算法的新型同伦法，解决解曲线折叠和解曲线追踪空间维数太大的问题，提高大规模电路的收敛效率；（3）对上述新型伪暂态法和同伦法的收敛性进行理论分析，并提出把智能寻优和伪暂态法、同伦法结合起来求解多个直流操作点。

In the development of communication industries and intelligent terminals, the analog circuit simulation technology is essential, since it is quite important for designing, testing, diagnosis and maintenance of life-cycle reliability in integrated circuit chips and electronic products. In circuit simulation, DC analysis is not only a basic assessment of circuit operation, but also a necessary foundation for other analysis methods, such as AC analysis and transient analysis. Therefore, the deep research on DC analysis is significant in theory and practice. To handle technical bottlenecks of current simulation algorithms and to further improve the convergence and convergence efficiency of large-scale circuit simulation, this project chooses pseudo-transient method and homotopy method as the breakthrough points and focuses on the following three topics: (1) A pseudo-transient method with strong damping effect and optimization of step control is proposed to solve the problems of oscillations, the discontinuities of solution curves and improper step setting; (2) With the decoupling idea and nonsingular dimension reduction algorithm, a new homotopy method is proposed to work out the problems of folds and the overlarge dimension of the solution curves; (3) Convergence theorems of the new algorithms are proved and an algorithm combining intelligent optimization algorithms with homotopy methods and pseudo-transient methods is proposed to find multiple dc solutions.