CALCULATION OF SENSITIVITIES FOR THE FREQUENCY-DOMAIN ELECTROMAGNETICPROBLEM

A simple derivation is presented for the computation of sensitivities needed to solve parametric inverse problems in electromagnetic inducti on. It is shown that sensitivities for any component of an electromagn etic field can be obtained by solving two boundary-value problems whic h are identical except for the specification of the source terms and ( possibly) prescribed boundary conditions. The electric fields from the se primal and auxiliary problems are multiplied and integrated to prod uce a numerical value for the sensitivity. Although the final formulae derived here are equivalent to those developed through the use of for mal adjoint or Green's functions approaches, our work does not require explicit derivation of the adjoint operator and boundary conditions a nd does not formally invoke reciprocity.