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.