Subwavelength Topology Optimization With Feature‐Mapping

ABSTRACT Acoustic topology optimization has been extensively studied since the earliest developments of structural optimization, and substantial progress has been made in the design of acoustic devices. More recently, wave‐focusing applications have attracted growing interest. In particular, sonic black hole (SBH) structures have gained traction for their ability to focus waves with wavelengths exceeding the structure's characteristic size. A key challenge in this context is the need to clearly distinguish between material/void phases. The solid isotropic material with penalization (SIMP) method introduces continuous pseudo‐densities, which can lead to intermediate material states that are beneficial for acoustic wave manipulation functions but unphysical. While this issue is often easily handleable in classical applications such as stiffness maximization, it becomes critical for subwavelength acoustic design. Our analysis reveals a strong dependence of transmission characteristics on both frequency and feature size, suggesting that filtering and projlts. In this work, we examine different filtering strategies by optimizing planar SBH‐type structures and develop a detailed understanding of acoustic behavior in the regime where the wavelength is significantly greater than the geometric scale. We employ the SIMP method, along with two feature‐mapping schemes, to obtain designs that achieve globally optimal performance for both single‐frequency and broadband focusing objectives. Finally, we analyze computational efficiency and provide practical recommendations for solving similar classes of acoustic optimization problems.