哈尔滨工业大学（深圳）学术讲座

演讲人Speaker：     Martin Berggren

题目Title:  Topology optimization of a true sonic black hole

时间Date： 2025 年 11 月 7 日       Time：10:00 – 11:00

地点Venue： T6506

内容摘要Abstract： 

A gradual tapering of a beam's or plate's thickness causes the transversal wave propagation speed to progressively slow down and the amplitude to increase. By analogy to what happens when approaching a gravitational black hole, the resulting device has been denoted a vibrational black hole. Mironov transferred this idea to longitudinal wave propagation and proposed a design of a waveguide sonic black hole. Unfortunately, although the suggested device is an effective broadband absorber, it contains none of the originally defining features of a "black hole", that is, (i) a gradual slowing of the propagation speed and (ii) a corresponding increase of its amplitude towards its distal end.

To design a device that accomplishes at least one of these features, we applied material distribution topology optimization to design a true wave-focusing device. Due to the potential presence of a large amount of surface area, it turned out to be crucial to account for viscothermal boundary-layer losses in the optimization. Also, to ensure a minimum radius of solid materials, we employed an approximate morphology closing operator based on a modified harmonic mean filter.

The optimized device exhibits a broadband focusing of the wave energy at the distal end. However, the speed of propagation is not well controlled. Carrying out time-domain simulations, we have recently shown that the propagation speed, although being reduced on average, varies wildly throughout the device.

Present investigations center around methods to impose in the optimization a slowing of the effective wave-propagation speed along the waveguide centerline. A promising method is based on a calculation of phase speeds from numerical solutions of the Helmholtz equation using ideas from geometric acoustics and ray theory.

个人简介(About the speaker):

Martin Berggren于1996年在美国德克萨斯州休斯敦的莱斯大学（Rice University）获得计算与应用数学博士学位。现为瑞典于默奥大学（Umeå University）计算机科学系的科学计算教授（Professor Emeritus）。此前，他曾任教于瑞典乌普萨拉大学（Uppsala University），并在瑞典国防研究局（Swedish Defense Research Agency）及美国阿尔伯克基的桑迪亚国家实验室（Sandia National Laboratories）担任研究职位。在其职业生涯中，Berggren 在其研究领域的顶级期刊上发表了约 70 篇学术论文，获得了多项科研资助。他最初的研究工作集中在航空应用中的计算空气动力学领域。自21世纪初以来，他的研究重点逐渐转向声波和电磁波传播问题，涵盖数学建模、数值算法的设计与分析，以及基于梯度的形状与拓扑优化在新领域中的应用。