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Shape Optimization of Electric and Magnetic System using Level Set Technique and Sensitivity Analysis

Y. Sun Kim, A. Weddemann, J. Jadidian, S. Khushrushahi, and M. Zahn
Dept. of Electrical Engineering and Computer Science
Cambridge, MA

The classical optimization method has been applied to many design problems for electromagnetic systems. One of its major difficulties is related to meshing problems arising from shape modifications. In order to circumvent these kinds of technical difficulties with moving mesh problems, several researches have tried to formulate shape optimization with fixed mesh analyses based on fixed grid finite elements. This approach was naturally associated with the level set description of geometry in order to provide an efficient treatment of problems involving geometry changes and discontinuities.

We employ the level set method to define evolving boundaries, since it provides a convenient means to describe closed interfaces of curves and surfaces. The level set function is expressed in the implicit form of a high-dimensional function, and then the boundary changes are traced by the deformation of this function.