Abstract In this paper we study the reconstruction of the acoustic field on an arbitrarily shaped vibrating surface using the Time domain Boundary Element Method (TBEM) based Near-field Acoustic Holography technique, or Inverse TBEM (ITBEM). The main focus of our study is the indirect formulation known as the single layer representation and the impact of the dicretization using higher order polynomial basis for both space and time. The solution of the resultant matrix system from this formulation contains a special sparse structure that can be efficiently implemented using Krylov subspace iterative methods like Least Squares QR (LSQR). We show, using numerical data, that the semi-convergent behavior of the LSQR iterations allows the effective mitigation of the ill-posed nature of the numerical solution to this matrix system. Similarly, we provide a numerical study of the ITBEM reconstruction when the signals contain problematic frequencies information. The numerical data is generated over a spherical geometry using Gaussian pulses.

中文翻译：

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基于近场声全息的时域边界元法的Krylov子空间迭代方法

摘要 在本文中，我们使用基于时域边界元法 (TBEM) 的近场声全息技术或逆 TBEM (ITBEM) 研究了任意形状振动表面上的声场重建。我们研究的主要焦点是称为单层表示的间接公式，以及对空间和时间使用高阶多项式基础的离散化的影响。从这个公式得到的矩阵系统的解包含一个特殊的稀疏结构，可以使用 Krylov 子空间迭代方法（如最小二乘 QR (LSQR)）有效地实现。我们使用数值数据表明，LSQR 迭代的半收敛行为可以有效缓解该矩阵系统数值解的不适定性质。相似地，当信号包含有问题的频率信息时，我们提供了 ITBEM 重建的数值研究。数值数据是使用高斯脉冲在球面几何上生成的。