Continuum Sensitivity Analysis and Shape Optimization of Dirichlet Conductor Boundary in Electrostatic System

This paper proposes an optimization method using the continuum sensitivity analysis for conductor shape design in the electrostatic system. The continuum sensitivity formula for a conductor shape is analytically derived by employing the material derivative concept from continuum mechanics and the adjoint variable technique. The geometry change of the conductor surface is determined by the velocity field from the derived sensitivity formula, and it is expressed by the level set method. Two numerical examples are tested to show the feasibility and usefulness of the proposed method.