含间断系数弹性结构的多重网格方法与数值模拟

journal6 ›› 2006, Vol. 27 ›› Issue (5): 76-81.

含间断系数弹性结构的多重网格方法与数值模拟

(湘潭大学土木工程与力学学院，湖南湘潭 411105)

出版日期:2006-09-25 发布日期:2012-06-29
作者简介:肖映雄(1970-)，男，湖南城步人，湘潭大学土木工程与力学学院讲师，博士生，主要从事计算力学教学与研究.
基金资助:
湖南省教育厅科学研究项目(03C451)

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

(Civil Engineering and Mechanics College,Xiangtan University,Xiangtan 411105,Hunan China)

Online:2006-09-25 Published:2012-06-29

摘要/Abstract

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.

关键词： 界面保持粗化, 弹性结构, 间断系数, 多重网格

Abstract: 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.

Key words: interface preserving coarsening, elastic structures, discontinuous coefficient, multigrid

肖映雄, 张平. 含间断系数弹性结构的多重网格方法与数值模拟[J]. journal6, 2006, 27(5): 76-81.

XIAO Ying-Xiong, ZHANG Ping. Multigrid Method and Numerical Simulation for Elastic Structures with Highly Discontinuous Coefficients[J]. journal6, 2006, 27(5): 76-81.

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