This article deals with the adaptive and approximative computation of the Lam\'e 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. Some adaptive algorithms based on hierarchical matrices and the adaptive cross approximation are proposed. At first, an adaptive matrix-vector multiplication scheme is introduced for the efficient treatment of multiplying discretizations with given data. The strategy, to reach this aim, is to use error estimators and techniques known from adaptivity. The case of approximating the system matrix appearing in the linear system of equations with this new type of adaptivity is also discussed.
翻译:本条涉及Lam\'e方程式的适应性和近似性计算。线性弹性方程式被视为边界整体方程式,并在确定边界元件方法(BEM)时予以解决。使用BEM,人们面临着一个公式系统的解决办法,这个公式系统有一个人口稠密的系统矩阵,一般费用非常高。提出了一些基于等级矩阵和适应性交叉近似的适应性算法。首先,引入了适应性矩阵-矢量倍增方案,以便有效地处理与特定数据相乘的离散。达到这个目标的战略是使用从适应性中知道的误差估计器和技术。还讨论了以这种新的适应性类型在线性方程式系统中出现的系统矩阵相近性的例子。