论文标题
平行的无基质高阶有限元求解器，用于相位场断裂问题
Parallel matrix-free higher-order finite element solvers for phase-field fracture problems
论文作者
论文摘要
相位场裂缝模型导致变异问题，可以写为耦合的变异平等和不平等系统。从数值上讲，可以使用galerkin有限元元素和原始二重式活动设置方法来处理此类问题。具体而言，可以使用低阶和高阶有限元素，而对于后者来说，迄今为止只有很少的研究。原始偶极活动集（半平滑牛顿）算法的离散版本中最耗时的部分是改变在每个半平滑牛顿步骤中更改线性系统的解决方案。我们为这些系统提出了一个新的无平行基质整体型多式预科器。我们提供两个数值测试，并讨论本文中提出的平行求解器的性能。此外，我们将新的预定器与文献中可用的块AMG预处理进行了比较。
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specifically, low-order and high-order finite elements may be employed, where, for the latter, only few studies exist to date. The most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm consists in the solutions of changing linear systems arising at each semi-smooth Newton step. We propose a new parallel matrix-free monolithic multigrid preconditioner for these systems. We provide two numerical tests, and discuss the performance of the parallel solver proposed in the paper. Furthermore, we compare our new preconditioner with a block-AMG preconditioner available in the literature.
