论文标题
快速多极边界元素方法，用于有限周期性结构的声学分析
Fast multipole boundary element method for the acoustic analysis of finite periodic structures
论文作者
论文摘要
在这项工作中，提出了两个快速的多极边界元素公式，用于有限周期性结构的线性时间谐波声学分析。有限的周期性结构由一个或多个周期性方向的有限数量的单位细胞复制组成。这样的结构可以设计为有效控制和操纵声波，并被称为声学超材料或声音晶体。我们的方法将几何形状细分为与单位单元相对应的框。应用边界元素离散化，并通过快速的多极扩展近似分离的框之间的相互作用。由于潜在的几何形状的周期性，扩展的某些操作员变成了块Toeplitz矩阵。这允许将矩阵矢量产物表示为循环卷积，从而大大降低了计算工作和整体内存要求。根据声学散射问题，显示了提出的技术的效率。此外，还对声音屏障的设计进行了研究，其中将类似墙壁的声音屏障的性能与两个声音晶体屏障的性能进行了比较。
In this work, two fast multipole boundary element formulations for the linear time-harmonic acoustic analysis of finite periodic structures are presented. Finite periodic structures consist of a bounded number of unit cell replications in one or more directions of periodicity. Such structures can be designed to efficiently control and manipulate sound waves and are referred to as acoustic metamaterials or sonic crystals. Our methods subdivide the geometry into boxes which correspond to the unit cell. A boundary element discretization is applied and interactions between well separated boxes are approximated by a fast multipole expansion. Due to the periodicity of the underlying geometry, certain operators of the expansion become block Toeplitz matrices. This allows to express matrix-vector products as circular convolutions which significantly reduces the computational effort and the overall memory requirements. The efficiency of the presented techniques is shown based on an acoustic scattering problem. In addition, a study on the design of sound barriers is presented where the performance of a wall-like sound barrier is compared to the performance of two sonic crystal sound barriers.
