This article deals with the efficient numerical treatment of the Lamé equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM). Using BEM, one is faced with the solution of a system of equations with a fully populated system matrix, which is in general very costly. In order to overcome this difficulty, adaptive and approximate algorithms based on hierarchical matrices and the adaptive cross approximation are proposed. These new methods rely on error estimators and refinement techniques known from adaptivity but are not used here to improve the mesh. We apply these new techniques to both, the efficient solution of Lamé equations and to the multiplication with given data.

中文翻译：

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线弹性中的自适应 H 矩阵计算

本文讨论 Lamé 方程的有效数值处理。线弹性方程被视为边界积分方程，并在边界元法（BEM）的设置中求解。使用 BEM，我们面临着求解具有完全填充的系统矩阵的方程组，这通常非常昂贵。为了克服这一困难，提出了基于层次矩阵和自适应交叉逼近的自适应近似算法。这些新方法依赖于自适应性中已知的误差估计器和细化技术，但此处不用于改进网格。我们将这些新技术应用于拉梅方程的有效求解以及与给定数据的乘法。