Advanced Electromagnetic System Analysis for Microwave Inverse and Design Problems

Abstract

<p> This thesis contributes significantly to the advancement of the response sensitivity analysis with time-domain electromagnetic (EM) solvers. The proposed self-adjoint sensitivity approaches achieve unprecedented computational efficiency. The response Jacobians are computed as a simple post-process of the field solution and the approaches can be applied with any commercial time-domain solver. The proposed sensitivity solvers are a breakthrough in the sensitivity analysis of high-frequency structures since they can be implemented as standalone software or plugin for EM simulators. The goal is to aid the solution of microwave design and inverse problems.</p> <p> The sensitivity information is crucial in engineering problems such as gradient-based optimization, yield and tolerance analyses. However, due to the lack of robust algorithms, commercial EM simulators provide only specific engineering responses not their sensitivities (or derivatives with respect to certain system parameters). The sensitivities are typically obtained by response-level finite difference (FD) approximations or parameter sweeps. For each design parameter of interest, at least one additional full-wave analysis is performed. Such approaches can easily become prohibitively slow when the number of design parameters is large.</p> <p> However, no extra system analysis is needed with the self-adjoint sensitivity analysis methods. Both the responses and their Jacobian are obtained through a single system analysis. In this thesis, two self-adjoint sensitivity solvers are introduced. They are based on a self-adjoint formulation which eliminates the need to perform adjoint system analysis. The first sensitivity solver is based on a self-adjoint formula which operates on the time waveforms of the field solution. Three different approaches associated with this sensitivity solver have been presented. The first approach adopts the staggered grid of the finite-difference time-domain (FDTD) simulation. We refer it as the original self-adjoint approach. The second approach is the efficient coarse-grid approach. It uses a coarse independent FD grid whose step size can be many times larger than that of the FDTD simulation. The third approach is the accurate central-node approach. It uses a central-node grid whose field components are collocated in the center of the traditional Yee cell.</p> <p> The second self-adjoint sensitivity solver is based on a spectral sensitivity formula which operates on the spectral components of the E-field instead of its time waveforms. This is a memory efficient wideband sensitivity solver. It overcomes the drawback associated with our first sensitivity solver whose memory requirements may become excessive when the number of the perturbation grid points is very large. The spectral approach reduces the memory requirements roughly from Gigabytes to Megabytes. The focus of this approach is on microwave imaging applications where our first sensitivity solver is inapplicable due to the excessive memory requirements. The proposed sensitivity solver is also well suited for microwave design problems.</p> <p> The proposed self-adjoint sensitivity solvers in this thesis are verified by numerous examples. They are milestones in sensitivity analysis because they have finally made EM simulation-based optimization feasible.</p>