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，尤其是与头部相关传递函数（HRTF）的计算，这些方法在3D中声源的定位中起着重要作用。与头部相关的传递功能描述了传入声音上头部，躯干，尤其是外耳（pinna）的滤波效果，可用于在虚拟声学中描述和模拟空间听力。对于声学问题的模拟，边界元素方法（BEM）是重要的工具。不幸的是，边界元素方法生成的矩阵是密集的，其尺寸随波数/频率而增长。为了克服这种障碍，我们将根据自适应小波方法和框架概念设计边界元素方法的有效变体。它们将特别调整为声学的要求，从而可以有效地计算高频的声场。我们将将小波压缩策略与自适应技术结合在一起，并设计适合当前问题的新框架，并研究数学和数值属性。 Biotop是一个多学科的项目，涉及数学，数字和声学建模。作为一个D-A-CH项目，它结合了德国研究小组的专业知识（自适应方案，规律性理论），奥地利（框架，HRTF的计算，声学建模）和瑞士（Wavelet Bem，Adaptitive）。