Efficient Two-Stage Optimization for Enhanced Broadband Absorption of Higher-Order PML

The development and application of the higher-order perfectly matched layer (HO-PML) often suffer from inadequate absorption performance due to empirically chosen PML parameters. However, using search algorithms to optimize PML parameters is time-consuming. To address these, we first introduce a new parameter adjustment strategy that includes 12 PML parameters, providing a comprehensive optimization framework. We then propose minimizing the maximum frequency-domain reflection coefficient (MFDRC) as the optimization objective to enhance the absorption performance of the HO-PML across a wide frequency range and over all time steps. To find the optimal PML parameter combination, we propose a two-stage optimization method combining the particle swarm optimization (PSO) with the artificial neural network (ANN). In the first stage, the PSO explores the wide search space and provides a set of high-quality inputs for the ANN, while in the second stage, the ANN captures the nonlinear relationship between these 12 PML parameters and the MFDRC and then predicts the optimal solution. A typical numerical example demonstrates that the proposed parameter adjustment strategy and optimization method improve the HO-PML absorption performance. Moreover, our optimization method significantly reduces the optimization time compared with existing search algorithms.