In real-world problems, inputs to computational electromagnetics (CEM)
simulations are often not known with full certainty (or precision): it is not
possible to manufacture geometry exactly to the required specifications;
results of material measurement systems have errors and uncertainty; and the
frequency of operation and angles of observation will not be perfect in
measurement systems. In spite of this, virtually all CEM algorithms presume a
single deterministic solution (often from presumed mean values of the uncertain
input parameters). The goal of this work is to devise a general approach for
incorporating uncertainties directly into computational electromagnetics tools.
A new approach to solve these types of problems is proposed in this
dissertation. This method involves a Small-Perturbation (SP) expansion
augmented with an Automatic-Differentiation (AD) solver and is denoted as the
Small-Perturbation Automatic-Differentiation or SPAD method.