Continuum Sensitivity Analysis for Shape Optimization of Transient Eddy Current Systems

This study proposes a shape sensitivity analysis for transient eddy current systems. The continuum sensitivity analysis is a deterministic optimization technique for designing the shape and topology of electromagnetic systems. Despite substantial research on the sensitivity analysis, most of the work has focused on static and steady-state issues. However, some problems require transient analysis. In this article, the shape sensitivity formula for a transient eddy current system was derived by the continuum approach using the adjoint variable technique and material derivative concept. In the sensitivity analysis using the derived sensitivity formula, the state variable equation is an initial-value problem to be solved forward in time. Conversely, the adjoint variable equation is a terminal-value problem to be solved backward in time. Three numerical examples were tested to demonstrate the feasibility and usability of the derived sensitivity formula.