Optimal shape design of 3-D nonlinear electromagnetic devices using parameterized design sensitivity analysis

A three-dimensional (3-D) shape optimization algorithm is developed by combining the geometric parameterization of the design surface using spline technique and design sensitivity analysis. The design surface is parameterized using Bezier spline or B-spline, and the control points of the spline are taken as the design variables. Considering nonlinearity of the material, the design sensitivities for the nodal points on the design surface and the adjoint variable are computed based on 3-D nonlinear finite-element method. The parameterized design sensitivities for the control points of the spline are computed from those for the nodal points. Through a numerical implementation, the developed algorithm is proved to guarantee a smooth design surface.