论文标题
基于层次矩阵和自适应交叉近似的波方程的边界元素方法
Boundary Element Methods for the Wave Equation based on Hierarchical Matrices and Adaptive Cross Approximation
论文作者
论文摘要
时间域边界元素方法（BEM）已成功用于声学，光学和弹性动力学，以数字解决瞬态问题。但是，由于必须在大量的时间步长或频率上计算填充的系统矩阵，因此存储要求是巨大的。在本文中，我们提出了一种新的近似正交法（CQM）动力BEM的近似方案，我们将其应用于由波方程控制的散射问题。我们在空间域中使用$ \ MATHCAL {H}^2 $ -MATRIX压缩，并在频域中采用自适应交叉近似（ACA）算法。通过这种方式，存储和计算成本大大降低，而该方法的准确性得以保留。
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices have to be computed for a large number of time steps or frequencies. In this article, we propose a new approximation scheme for the Convolution Quadrature Method (CQM) powered BEM, which we apply to scattering problems governed by the wave equation. We use $\mathcal{H}^2$-matrix compression in the spatial domain and employ an adaptive cross approximation (ACA) algorithm in the frequency domain. In this way, the storage and computational costs are reduced significantly, while the accuracy of the method is preserved.
