Acoustic black holes (ABHs) are a passive damping mechanism with remarkable wave-manipulation properties, attracting significant research interest. Mironov (1988) introduced the fundamental concepts by analyzing a tapered beam with a thickness that decreases quadratically [1]. The gradual reduction in thickness slows the propagation of elastic waves, concentrating mechanical energy near the ABH tip. However, efficient damping requires this energy to be dissipated locally. It should be noted that Krylov (2004) coined the term ABH only several years after its working principle was first described [2]. Despite growing interest, most studies on ABHs do not focus on numerical modeling, leaving details concerning the temporal and spatial discretizations unclear [3]. Wave propagation analysis remains computationally demanding, making it essential to balance accuracy and efficiency. Therefore, we benchmark commercial finite element solvers to assess their performance in ABH simulations. In this context, we consider time-implicit analyses with Ansys and COMSOL, and time-explicit simulations with LS-Dyna and COMSOL. Here, it is not a priori clear whether low- or high-order finite elements, or explicit versus implicit time integration, yield the most efficient results. Setting up an efficient model thus requires expertise in both finite element methods and time-integration schemes. Consequently, we investigate combinations of finite elements and transient solvers to provide guidelines for spatial and temporal discretizations that enable time-efficient ABH simulations. Focusing on an ABH of quadratically decreasing thickness, we conduct convergence studies using the L2-norm of displacement errors to derive practical recommendations. We incorporate high-order elements and high-order time-integration schemes, following the high-order in space and time paradigm, previously unexamined in ABH analysis. Our results offer a valuable resource for practitioners and researchers studying ABH systems. References [1] M. A. Mironov, Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval, Soviet Physics–Acoustics [2] V. V. Krylov, New type of vibration dampers utilising the effect of acoustic ’black holes’, Acta Acustica united with Acustica [3] . Pelat, F. Gautier, S. C. Conlon, F. Semperlotti, The acoustic black hole: A review of theory and applications, Journal of Sound and Vibration