An Open-Source Two-Stage PS–NM Workflow for PDE-Constrained Acoustic Shape Optimization

This study introduces an open-source hybrid shape optimization workflow for acoustic wave problems that integrates acoustic wave propagation analysis with a two-stage optimization strategy. A coarse Parameter Sweep (PS) is first used for feasibility screening and global exploration, followed by derivative-free local refinement using the Nelder–Mead (NM) method. The framework is demonstrated on three benchmark problems: (i) an acoustic horn optimized for improved impedance matching and reduced reflections, (ii) a noise barrier reshaped to minimize acoustic pressure in the shadow zone, and (iii) a crescent-shaped scatterer designed to attenuate downstream pressure amplitude. Across all cases, the PS–NM strategy achieved lower objective values than baseline-initialized local optimization, at the expense of increased computational cost. All analyses were performed in the open-source FEniCS environment within Jupyter Notebooks. Comparisons with published results support the accuracy and consistency of the implementation. By combining accessibility with flexibility, the framework provides a reproducible methodology for acoustic shape optimization. Potential extensions include multi-objective formulations, frequency-adaptive designs, improved constraint-handling strategies, and integration with metamaterial concepts.