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 highly complex anisotropic character as well as nonlinear media, there are some places where one could cite the desire to maintain a variational approach. It is for these cases that we here address the properties of the auxiliary method for treating differing degrees of anisotropy, including but not limited to gyroelectric, gyromagnetic chiral, gyroelectromagnetic, gyroelectrochiral, gyromagnetochiral, and gyroelectromagnetochiral. What the adjoint method is capable of doing and its limitations will be discussed in view of the auxiliary method. Issues such as inner product boundary conditions, adjoint media, adjoint fields, non-self-adjointness, nonhermiticity, auxiliary vector f function, to name a few, will be considered. These matters have particular significance for problems being solved today using intensive numerical techniques such as finite difference and finite element methods being simulated on PC, MAC, workstation, and mainframe platforms