The adjoint variable method for frequency-independent constitutive parameters
In this chapter, we show how adjoint sensitivity analysis techniques can be applied to computational electromagnetics problems. We focus in this chapter on linear, isotropic, and nondispersive electromagnetic structures. In this case, the properties of all materials in the computational domain do not depend on the field magnitude, the excitation polarization, or the excited frequency band. We adopt a step-by-step approach for introducing the basic concepts. First, we address the 1D finite difference time domain (FDTD) case and show how adjoint sensitivities are estimated. This case is illustrated through a numerical example. We then address the 2D TMz case. A full derivation of the adjoint variable method is given. We show that using a similar formulation to the 1D case, the sensitivities of a general objective function with respect to all parameters are estimated using one extra simulation. The 2D transverse electric to z (TEz) is similar to the 2D transverse magnetic to z (TMz) and will not be addressed here. Two numerical examples are presented to illustrate the 2D case. Finally, we address the full 3D case and show that the same concept applies to full 3D problems.