Design of electromagnetic devices using sensitivities computed with the adjoint variable method

The adjoint variable method allows the sensitivities with respect to all system parameters to be computed at the cost of a solution to an adjoint problem. The present paper derives expressions for the sensitivities in terms of the fields of the original and the adjoint problems. Expressions for the sources to the adjoint problem are also derived. These expressions are then applied to an example in which the objective is to maximize the levitating force on a conducting ring