论文标题
自适应$ \ MATHCAL {H} $ - 线性弹性中的矩阵计算
Adaptive $\mathcal{H}$-Matrix Computations in Linear Elasticity
论文作者
论文摘要
本文介绍了Lamé方程的自适应和近似计算。线性弹性的方程式被视为边界积分方程，并在边界元素方法（BEM）的设置中求解。使用BEM，一个面对具有完全填充的系统矩阵的方程系统的解决方案，总体上非常昂贵。提出了一些基于层次矩阵和自适应交叉近似的自适应算法。首先，引入了自适应矩阵矢量乘法方案，以有效地处理给定数据的离散化。达到此目标的策略是使用从适应性中知道的误差估计器和技术。还讨论了使用这种新型适应性的方程式中出现的系统矩阵的情况。
This article deals with the adaptive and approximative computation 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. 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.
