论文标题
截短的非平滑牛顿牛顿多果片，用于分析，用于相位场脆性骨折问题
Truncated Nonsmooth Newton Multigrid for phase-field brittle-fracture problems, with analysis
论文作者
论文摘要
我们提出了截短的非平滑牛顿多摩托方法（TNNMG），作为解决小型微分裂缝相位场方程的空间问题的求解器。 tnnmg是一种非平滑的多裂体方法，可以解决双线性的非平滑度最小化问题，并具有线性时间复杂性。它利用了问题固有的变异结构，并直接对损害变量进行了侧面的不可逆性约束，而无需正则化或引入本地历史领域。在论文中，我们介绍了该方法，并显示如何将其应用于几种已建立的相位脆性断裂模型。然后，我们证明了求解器与任何负载和初始迭代的空间问题的非平滑欧拉 - 拉格兰奇方程的解决方案的收敛。在途中，我们显示了此处考虑的模型的几种至关重要的凸度和规律性。与操作员分解算法的数值比较显示出相当大的速度增加，而不会损失稳健性。
We propose the Truncated Nonsmooth Newton Multigrid Method (TNNMG) as a solver for the spatial problems of the small-strain brittle-fracture phase-field equations. TNNMG is a nonsmooth multigrid method that can solve biconvex, block-separably nonsmooth minimization problems with linear time complexity. It exploits the variational structure inherent in the problem, and handles the pointwise irreversibility constraint on the damage variable directly, without regularization or the introduction of a local history field. In the paper we introduce the method and show how it can be applied to several established models of phase-field brittle fracture. We then prove convergence of the solver to a solution of the nonsmooth Euler--Lagrange equations of the spatial problem for any load and initial iterate. On the way, we show several crucial convexity and regularity properties of the models considered here. Numerical comparisons to an operator-splitting algorithm show a considerable speed increase, without loss of robustness.
