Continuum Sensitivity Analysis for Shape optimization of Transient Eddy Current System

This paper proposes a shape sensitivity analysis for the transient eddy current system. The continuum shape sensitivity of the transient eddy current system is derived by using the material derivative concept and the adjoint variable technique. In the continuum shape sensitivity analysis, the state variable equation is an initial-value problem to be solved forward in time. In contrast, the adjoint variable equation is a terminal-value problem, which is solved backward in time. With the state and adjoint variables, the design velocity of the shape sensitivity formula is evaluated and coupled with the level set equation to represent the deforming geometry. A numerical example having the known solution is tested to show the feasibility of the derived sensitivity formula.