Adaptive Wavelet and Frame Techniques for Acoustic BEM

声学边界元法的自适应小波和框架技术

• 批准号: 223613512
• 负责人: Professor Dr. Stephan Dahlke
• 金额: --
• 依托单位: Fachbereich Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/223613512?language=en
• 关键词: Adaptive; Wavelet; Frame; Techniques; Acoustic

In BIOTOP, we will develop new methods to model 3D acoustic wave problems, especially the calculation of head related transfer functions (HRTFs), which play an important role in the localization of sound sources in 3D. Head related transfer functions describe the filtering effect of the head, the torso, and especially the outer ear (pinna) on incoming sounds and can be used to describe and simulate spatial hearing in virtual acoustics. For the simulation of acoustic problems, the boundary element method (BEM) is an important tool. Unfortunately, the matrices generated by the boundary element method are dense and their dimension grows with the wavenumber/frequency. To overcome this obstruction, we will design efficient variants of the boundary element method based on adaptive wavelet methods and the concept of frames. They will be particularly tuned to the requirements in acoustics, thus allowing an efficient computation of sound fields also for high frequencies. We will combine wavelet compression strategies with adaptive techniques and design new frames adapted to the problem at hand, and investigate the mathematical and numerical properties. BIOTOP is a multi-disciplinary project by necessity, involving mathematics, numerics and acoustical modeling. As a D-A-CH project, it combines the expertise of the research groups from Germany (adaptive schemes, regularity theory), Austria (frames, calculation of HRTFs, acoustic modeling) and Switzerland (wavelet BEM, adaptivity).

在BIOTOP中，我们将开发新的方法来模拟3D声波问题，特别是头部相关传递函数（HRTF）的计算，这在3D声源定位中起着重要作用。头部相关的传递函数描述了头部、躯干、特别是外耳（耳廓）对传入声音的滤波效果，并且可以用于描述和模拟虚拟声学中的空间听觉。对于声学问题的模拟，边界元法是一种重要的工具。不幸的是，由边界元法生成的矩阵是稠密的，并且它们的维数随着波数/频率而增长。为了克服这个障碍，我们将设计有效的变种的边界元法的基础上自适应小波方法和框架的概念。他们将特别调整到声学的要求，从而允许高频率的声场的有效计算。我们将结合联合收割机小波压缩策略与自适应技术和设计新的框架，适应手头的问题，并调查的数学和数值特性。BIOTOP是一个多学科的项目，涉及数学，数值和声学建模。作为一个D-A-CH项目，它结合了来自德国（自适应方案、规律性理论）、奥地利（框架、HRTF计算、声学建模）和瑞士（小波边界元法、自适应性）的研究小组的专业知识。