论文标题
使用宏元素几乎不可压缩的弹性的强大的多移民方法
Robust multigrid methods for nearly incompressible elasticity using macro elements
论文作者
论文摘要
我们为与宏元素结构的网格上的几乎不可压缩的线性弹性方程式的Scott-Vogelius离散化提供了一个独立于网状和参数的多机求解器。离散化在中度多项式程度下实现了限制差异约束的准确表示。放松和多移民转移操作员都利用宏观结构来提高鲁棒性和效率。为了放松，我们使用每个宏单元上的局部fortin运算符的存在来构建一个局部空间分解，并具有参数 - 射击收敛。对于转移，我们通过在每个粗大宏单元上执行小的局部求解来构建一个可靠的延长操作员。数值实验证实了算法的两个组成部分的必要性。
We present a mesh-independent and parameter-robust multigrid solver for the Scott-Vogelius discretisation of the nearly incompressible linear elasticity equations on meshes with a macro element structure. The discretisation achieves exact representation of the limiting divergence constraint at moderate polynomial degree. Both the relaxation and multigrid transfer operators exploit the macro structure for robustness and efficiency. For the relaxation, we use the existence of local Fortin operators on each macro cell to construct a local space decomposition with parameter-robust convergence. For the transfer, we construct a robust prolongation operator by performing small local solves over each coarse macro cell. The necessity of both components of the algorithm is confirmed by numerical experiments.
