<p> This thesis contributes to the development of a novel electromagnetic (EM) time-domain computational approach, the self-adjoint variable method, for the scattering parameter (S-parameter) sensitivity analysis of high frequency problems. </p> <p> The design sensitivity analysis provides sensitivity information in the form of the response gradient (response Jacobian). For that, various techniques are used, ranging from finite-difference approximations to quadratic and spline interpolations. However, when the number of design parameters becomes large, the simulation time would become unaffordable, which is especially the case with EM simulations. The proposed self-adjoint sensitivity analysis (SASA) approach aims at providing sensitivity information efficiently without sacrificing the accuracy. Its efficiency lies in the fact that regardless of the number of design parameters, only one simulation of the original structure is required- the one used to compute the S-parameters. Thus, the sensitivity computation has negligible overhead. At the same time, it has second-order accuracy. </p> <p> Currently, commercial EM simulators provide only specific engineering responses, such as Z- or S-parameters. No sensitivity information is actually made available. With the SASA approach, the only requirement for the EM solver is the ability to access the field solution at the perturbation grid points. This feature is generally available with all time-domain EM simulators. The manipulation of the field solutions in this approach is simple and it adds practically negligible overhead to the -simulation time. </p> <p> We confirm the validity of this approach for both the shape and constitutive parameters of the design structures. 2-D examples including metallic and dielectric details are presented, using the field solutions from an in-house time-domain solver. We also explore the feasibility of implementing this approach with one of the commercial solvers, XFDTD v. 6.3. </p> <p> Suggestions for future research are provided. </P> / Thesis / Master of Applied Science (MASc)

<p> This thesis proposes a sensitivity solver for frequency-domain electromagnetic (EM) simulators based on volume methods such as the finite-element method (FEM). The proposed sensitivity solver computes S-parameter Jacobians directly from the field solutions available from the EM simulation. It exploits the computational efficiency of the self-adjoint sensitivity analysis (SASA) approach where only one EM simulation suffices to obtain both the responses and their gradients in the designable parameter space. The proposed sensitivity solver adopts the system equations of the finite-difference frequency-domain (FDFD) method.</p> <p> There are three major advantages to this development: (1) the Jacobian computation is completely independent of the simulation engine, its grid and its system equations; (2) the implementation is straightforward and in the form of a post-processing algorithm operating on the exported field solutions; and (3) it is computationally very efficient-time requirements are negligible in comparison with conventional field-based optimization procedures utilizing Jacobians computed via response-level finite differences or parameter sweeps.</p> <p> The accuracy and the efficiency of the proposed sensitivity solver are verified in the sensitivity analysis and the gradient-based optimization of filters and antennas. Compared to the finite-difference approximation, drastic reduction of the time required by the overall optimization process is achieved. All examples use a commercial finite-element simulator.</p> <p> Suggestions for future research are provided.</p> / Thesis / Master of Applied Science (MASc)