COMPARISON OF THE AUXILIARY VECTOR FUNCTION AND ADJOINT METHODS IN SOLVING ANISOTROPIC MEDIA ELECTROMAGNETIC PROBLEMS

Although weighted residual techniques are extremely general and may be applied to both very arbitrary linear media of higly complex anisotro pic character as well as nonlinear media, there are some place where o ne could cite the desire to maintain a variational approach. It is for these cases that we here address the properties of the auxiliary meth od for treating differing degrees of anisotropy, including but not lim ited to gyroelectric, gyromagnetic, chiral, gyroelectromagnetic, gyroe lectrochiral, gyromagnetochiral, and gyroelectromagnetochiral. What th e adjoint method is capble of doing and its limitations will be discus sed in view of the auxiliary method. Issues such as inner product boun dary conditions, adjoint media, adjoint fields, non-self-adjointness, nonHermiticity, auxiliary vector f function, to name a few, will be co nsidered. These matters have particular significance for problems bein g solved today using intensive numerical techniques such as finite dif ference and finite element methods being simulated on PC, MAC, worksta tions, and mainframe platforms.