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.
