Adjoint Sensitivity Analysis of Time-Domain Responses Exploiting Time-Domain Transmission Line Modeling Method

Abstract

<p>The traditional approach for estimating sensitivities utilizes finite difference (FD) approximations which are time-intensive even for simple problems. This involves perturbing each design parameter in the forward and/or backward directions and simulating the perturbed structures. For a problem with <em>N</em> optimizable parameters, this approach requires at least <em>N</em>+1 simulations. If<em> N</em> is large, this approach may easily become impractical due to the intensive simulation time.</p> <p>The Adjoint Variable Method (A VM) aims at obtaining the response sensitivities using at most one extra simulation regardless of the number of designable parameters. The field information is stored at specific points related to each parameter in both the original and adjoint simulations. This approach was applied to sensitivity analysis of scalar objective functions and frequency domain responses.</p> <p>This thesis addresses a new A VM algorithm for estimating time domain response sensitivities using time domain transmission-line modeling (TD-TLM) method. Our algorithm obtains the sensitivities of any electromagnetic time domain response over the whole simulation time with respect to all parameters using only one extra time domain simulation. A very good match is obtained between our sensitivity estimates and those obtained through the accurate and time-intensive central difference approximation.</p> <p>One of the motivations for sensitivity analysis is gradient-based optimization. The optimization process speeds up by using our A VM algorithm for gradient estimation. In this literature, we will implement gradient-based optimization using our AVM through different applications including microwave imaging problem. The results show good match between the sensitivities obtained using our A VM approach and those obtained using the more expensive finite difference approximation.</p>