The acoustic wave equation is solved in time domain with a boundary element formulation. The time discretisation is performed with the generalised convolution quadrature method and for the spatial approximation standard lowest order elements are used. Collocation and Galerkin methods are applied. In the interest of increasing the efficiency of the boundary element method, a low-rank approximation such as the adaptive cross approximation (ACA) is carried out. We discuss about a generalisation of the ACA to approximate a three-dimensional array of data, i.e., usual boundary element matrices at several complex frequencies. This method is used within the generalised convolution quadrature (gCQ) method to obtain a real time domain formulation. The behaviour of the proposed method is studied with three examples, a unit cube, a unit cube with a reentrant corner, and a unit ball. The properties of the method are preserved in the data sparse representation and a significant reduction in storage is obtained.

翻译：声波方程采用边界元公式在时域内求解。时间离散化采用广义卷积求积方法，空间近似使用标准最低阶单元。应用配置法和伽辽金法。为提高边界元方法的效率，采用自适应交叉逼近（ACA）等低秩逼近技术。我们讨论了一种三维数据阵列（即多个复频率下的常规边界元矩阵）的ACA推广方法。该方法用于广义卷积求积（gCQ）框架，以得到实时的时域公式。通过三个算例（单位立方体、带凹角的单位立方体及单位球）研究该方法的表现。在数据稀疏表示中，方法特性得以保持，且存储量显著降低。