Shape Sensitivity Analysis for Optimal Design of Time-Harmonic Electroquasistatic System based on Continuum Approach

This paper proposes a continuum-based sensitivity analysis for an optimal shape design of a time-harmonic electroquasistatic (EQS) system. The material derivative concept, which originates from continuum mechanics, is employed for deriving the shape sensitivity formula. All the boundaries of the EQS system are considered its design variables. The Lagrange multiplier method, adjoint variable technique, and variational identity are sequentially applied to the material derivative of an augmented objective function. Thereby, the sensitivity formula is obtained in an analytical form and expressed by a boundary integral. Since the continuum shape sensitivity is evaluated prior to the discretization process of the finite element method (FEM), it can be easily and accurately calculated using commerical FEM software. The smooth expression of the shape-variation is implemented by combining the shape sensitivity with the level-set method. The shape optimization problem in the three-dimension is presented to demonstrate the theoretical validity and numerical feasibility of this study.