Shape and material optimization using gradient methods and the adjoint problem in time and frequency domain

Purpose: Shape and material parameters have major influence on the performance of electromagnetic components. Optimization of these parameters is therefore vital in electromagnetic design. Reduction of the radar cross section (RCS) for aircraft and frequency selective surfaces are two well known examples. Shape and materials optimization is performed for different scatterers in 2D. Design/methodology/approach: Continuum design sensitivities for microwave problems are applied for the gradient-based optimization of scatterers' shape and material parameters. The goal function is chosen to be an average of the monostatic RCS for a sector of incident angles over a frequency band. Numerical tests are presented for 2D scatterers and, specifically, a perfectly electrically conducting scatterer and an absorber on the front edge of an airplane wing are considered. The results are compared with theoretical findings and results in the open literature. Findings: It is demonstrated that a dense frequency sampling of the goal function over a wide frequency band relaxes the requirements on the angular resolution. The broad band requirements on the RCS also avoids corrugations without the resorting to regularization methods and penalty terms added to the goal function. The optimization algorithm refines, in a small number of iterations, the initial geometry of the scatterer to an optimized design with strongly reduced RCS. Originality/value: Shape and material parameters have major influence on the performance of electromagnetic components. Optimization of these parameters for scatterers demonstrates that a densely evaluated goal function over a broad frequency band has the advantages of: lowering the requirements on angular resolution; avoiding corrugations; and regularizing the problem by the broad frequency band requirements which often are naturally included in the performance specification of electromagnetic devices.