Ing. Štěpán Bosák

This paper presents a novel bi-level topology optimization strategy within the method-of-moments paradigm. The proposed approach utilizes an auxiliary variables called edge resistivities related to the Rao–Wilton–Glisson method-of-moments basis functions, for a definition of a fast local optimization algorithm. The local algorithm combines automatic differentiation with adaptive gradient descent. A Bayesian optimization scheme is applied on top of the local algorithm to search for an optimum position of the delta-gap feeding and optimizer hyperparameters. The strength of the algorithm is demonstrated on Q-factor minimization for electrically small antennas. Auxiliary edge resistivity topology optimization outperforms current state-of-the-art topology optimization methods, including material density-based approaches and memetic schemes, in terms of convergence. However, due to the nature of gradient descent, careful tuning of the optimizer hyperparameters is required. Furthermore, the proposed method solves the known binarization issue. Two designs that achieved self-resonance and approached the Q-factor lower bound were further assessed in CST Microwave Studio.

Antenna inverse design has gained significant popularity, yet it often faces challenges with slow convergence to optimal solutions. This paper presents a novel deep-learning algorithm for accelerated Q-factor evaluation based on the Method-of-Moments (MoM). The proposed deep neural network directly processes triangular antenna meshes to estimate the vector of current expansion coefficients, effectively replacing the traditional impedance matrix inversion required in MoM. The Q-factor is subsequently computed. For this purpose, we introduce QfResNET, a Residual Network (ResNET) architecture featuring an upsampling convolutional network and the GELU activation function. Antennas are represented as multi-channel 2D arrays, preserving the neighborhood relationships in the antenna mesh and labeled with Q-factors derived through MoM calculations. Our results demonstrate that QfResNET achieves a speed-up of up to 957% compared to MoM. However, for coarser antenna meshes, the deep neural network does not offer a significant advantage.