On Some Identities for Integral Operators in Computational Electromagnetics

A series of new identities are proposed for commonly used integral operators in electromagnetics. These identities are closely related to the classical Calderón identities that have been extensively studied because of their applications as an analytical preconditioners in solving surface integral equations. We report on new identities by separating the real and imaginary parts of the free space Green function G(R) = exp(-ik R)/ 4π R, where R = |r - r'| is the distance between source point r' and observation point r. Moreover, we use some conclusions in the characteristic mode theory (CMT) to derive more identities that are closely related to the Calderón identities, which have theoretical and practical implications.