含间断系数弹性结构的多重网格方法与数值模拟

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.

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

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.