Applications of a fast multipole Galerkin in boundary element method in linear elastostatics
Applications of a fast multipole Galerkin in boundary element method in linear elastostatics
复制标题
快速多极伽辽金在线性弹性静力学边界元法中的应用
DOI：
10.1007/s00791-005-0010-9
复制
发表时间：
2005
影响因子：
--
通讯作者：
W. Wendland
中科院分区：
文献类型：
--
作者：
G. Of;O. Steinbach;W. Wendland
边界元法为求解线性弹性静力学边值问题，特别是复杂三维结构的边值问题提供了强有力的工具。与导致稠密刚度矩阵的标准Galerkin方法相比，在快速边界元方法（例如快速多极子方法）中，可以以几乎线性的复杂性实现矩阵向量乘积的应用。由于线性弹性静力学的所有边界积分算子都可以约化为拉普拉斯算子，因此只需离散相应的拉普拉斯算子的单层和双层位势。这种技术的结果在一个快速多极方法，这是一个有效的工具，在工程和工业应用中的弹性应力场的模拟。
AbstactBoundary element methods provide a powerful tool for solving boundary value problems of linear elastostatics, especially in complicated three–dimensional structures. In contrast to the standard Galerkin approach leading to dense stiffness matrices, in fast boundary element methods such as the fast multipole method the application of matrix–vector products can be realized with almost linear complexity. Since all boundary integral operators of linear elastostatics can be reduced to those of the Laplacian, the discretization of the corresponding single and double layer potentials of the Laplace operator has to be employed only. This technique results in a fast multipole method which is an efficient tool for the simulation of elastic stress fields in engineering and industrial applications.