Sensitivity analysis based on analytic approach for shape optimization of electromagnetic devices: interface problem of iron and air

The material derivative concept of continuum mechanics and the adjoint variable method of design sensitivity analysis are used to express the relation between the change of shape and that of the objective function. The explicit sensitivity formula for the interface variation between iron and air is derived in a two-dimensional electromagnetic system. Implementation of the sensitivity analysis is carried out with existing finite element codes. The sensitivity analysis is applied to the pole optimization of a quadrupole.