Electromagnetic optimisation using sensitivity analysis in the frequency domain

Gradient-based optimisation relies on the response Jacobian whose evaluation constitutes a major computational overhead in full-wave numerical analysis. Adjoint-based techniques may offer numerically efficient solutions, but their implementation is too involved in the case of full-wave computations. A simple approach that uses the self-adjoint sensitivity analysis and Broyden's update is proposed. The overhead of the Jacobian computation is greatly reduced because an adjoint system analysis is not needed and because Broyden's update is used to compute the system matrix derivatives. To improve the robustness of the Broyden update in the sensitivity analysis, we propose a switching criterion between the Broyden and the finite-difference estimation of the system matrix derivatives. We illustrate and validate the proposed method using full-wave commercial electromagnetic solvers based on the finite-element method as well as on the method of moments. Different gradient-based optimisation algorithms are exploited in the examples where efficiency is compared in terms of CPU time savings.