VPW: Homotopy Methods for Analysis and Simulation of Electronic Circuits

寻找电子电路的直流工作点、稳态和瞬态响应是电路仿真的基本任务，涉及非线性微分/代数方程。 传统的方法求解这样的方程组往往失败，难以收敛，往往不能找到所有的解决方案。 Trajkovic博士将研究同伦方法在解决描述电力电子和开关电路以及电力系统流方程的非线性方程中的应用，这些方程传统上会造成仿真困难。 同伦实验可能会导致更好的电路仿真工具的发展，并更好地理解同伦方法和非线性电路的行为之间的关系。 Trajkovic博士将在德国伍珀塔尔大学电气工程系工作三个月，与Wolfgang马西斯教授及其学生合作。 他们的“电子电路理论和计算机辅助设计”小组积极从事电路理论和模拟的研究。 这将是她在伯克利的研究活动的延续，重点是基于各种同伦实验的理论工作。 互动活动包括：教授“高级电路理论”的研究生课程，向学生介绍分析结果，提供对电子电路复杂行为的见解和理解;举办“同伦方法在解决工程问题中的应用”系列讲习班/研讨会，特别强调电路模拟和求解描述非线性电路的方程;组织非正式的讲习班，让女学生做报告，并就她们的研究和职业目标得到建议。

Finding dc operating points, steady state, and transient responses of electronic circuits are essenntial tasks in electrical circuit simulation and involve nonlinear differential/algebraic equations. Traditional methods for solving such systems of equations often fail, are difficult to converge, and, often cannot find all the solutions. Dr. Trajkovic will investigate the application of homotopy methods to solving nonlinear equations describing power electronic and switching circuits and power systems flow equations, that traditionally pose simulation difficulties. Experiments with homotopies may lead to the development of better circuit simulation tools and to better understanding of relationships between homotopy methods and the behavior of nonlinear circuits. Dr. Trajkovic will spend three months with the Electrical Engineering Department at the University of Wuppertal, Germany where she will collaborate with Professor Wolfgang Mathis and his students. Their "Theory and Computer Aided Design of Electronic Circuits " group actively pursues research in circuit theory and simulation. This will be a continuation of her research activities at Berkeley, with emphasis on theoretical work based on experiments with various homotopies. Interactive activities include: teaching a graduate course in "Advanced Circuit Theory" that will introduce students to analytical results that provide insights and understanding of complex behavior of electronic circuits; holding a workshop/seminar series on "Application of Homotopy Methods in Solving Engineering Problems," with special emphasis on circuit simulation and solving equations describing nonlinear circuits; and organizing informal workshops where female students make presentations and get advice about their research and career goals.