含间断系数弹性结构的多重网格方法与数值模拟  

Multigrid Method and Numerical Simulation for Elastic Structures with Highly Discontinuous Coefficients

作　　者：肖映雄[1] 张平[1] 

机构地区：[1]湘潭大学土木工程与力学学院,湖南湘潭411105

出　　处：《吉首大学学报（自然科学版）》2006年第5期76-81,共6页Journal of Jishou University(Natural Sciences Edition)

基　　金：湖南省教育厅科学研究项目(03C451)

摘　　要：提出了求解含间断系数弹性力学问题的界面保持粗化多重网格方法,该粗化方法在选取粗网格节点时保证在每一个网格层上能保持界面的实际形状,同时可以捕获位移解函数沿界面处导函数的不连续行为,这样只需要构造简单的插值算子,并选取点块Gauss-Seidel作磨光迭代,就能达到理想的多重网格收敛效率.数值实验结果表明,这种界面保持粗化多重网格方法的收敛性不依赖于网格规模及间断系数的大小,具有很好的数值稳定性.An interface preserving coarsening multigrid method is proposed for the solution of elastic structures with highly discontinuous coefficients.It selects coarse grid points so that all the coarse grids are aligned with the interface for regular interface elastic proplems on structured grids.As a result,multigrid with simple linear interpolation and point block Gauss-Seidel smoothing is sufficient to obtain the usual rapid convergence.Numerical results show that the convergence rate of the resulting multigrid method is independent of the mesh size and the size of the jumps at the interfaces.

关 键 词：界面保持粗化 弹性结构 间断系数 多重网格 

分 类 号：O241.6[理学—计算数学] O344.1[理学—数学]