Matrix-free multigrid solvers for phase-field fracture problems
Matrix-free multigrid solvers for phase-field fracture problems
复制标题
用于相场断裂问题的无矩阵多重网格求解器
DOI：
10.1016/j.cma.2020.113431
复制
发表时间：
2019
影响因子：
7.2
通讯作者：
T. Wick
中科院分区：
文献类型：
--
作者：
D. Jodlbauer;U. Langer;T. Wick
在这项工作中，我们提出了用几何多重网格法求解整体准静态相场断裂模型的无矩阵解的框架。在有限元方法中使用标准的基于矩阵的方法需要大量内存，这最终会成为一个严重的瓶颈。无矩阵方法克服了这一问题，并极大地减少了所需内存量，从而允许在可用硬件上解决更大的问题。一个关键的挑战是关于裂纹的不可逆性，为此采用了原始-对偶有效集方法。在这里，精细网格的活动集值必须在多重网格算法的较粗级别上可用。发展的多重网格法为广义最小残差(GMRES)求解器提供了一个预条件。该方法用于求解牛顿方法中的线性方程组，用于处理整体的非线性整体离散位移/相场公式。几个数值例子证明了我们的解决方案技术的性能和稳健性。通过网格加密研究、相场正则化参数的变化、线性和非线性求解器迭代次数的变化以及一些并行性能，验证了所提出的求解器对单裂缝、多加压裂缝和三维L板状试件的有效性。
In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix-based approach within the Finite Element Method requires lots of memory, which eventually becomes a serious bottleneck. A matrix-free approach overcomes this problem and greatly reduces the amount of required memory, allowing to solve larger problems on available hardware. One key challenge is concerned with the crack irreversibility for which a primal–dual active set method is employed. Here, the active set values of fine meshes must be available on coarser levels of the multigrid algorithm. The developed multigrid method provides a preconditioner for a generalized minimal residual (GMRES) solver. This method is used for solving the linear equations inside Newton’s method for treating the overall nonlinear-monolithic discrete displacement/phase-field formulation. Several numerical examples demonstrate the performance and robustness of our solution technology. Mesh refinement studies, variations in the phase-field regularization parameter, iterations numbers of the linear and nonlinear solvers, and some parallel performances are conducted to substantiate the efficiency of the proposed solver for single fractures, multiple pressurized fractures, and a L-shaped panel test in three dimensions.
DOI：
10.1016/j.cma.2015.09.021
发表时间：
2016-06-01
影响因子：
7.2
作者：
Miehe, Christian;Mauthe, Steffen
通讯作者：
Mauthe, Steffen
DOI：
10.1145/3325864
发表时间：
2017-11
期刊：
ACM Transactions on Mathematical Software (TOMS)
影响因子：
--
作者：
M. Kronbichler;K. Kormann
通讯作者：
M. Kronbichler;K. Kormann
DOI：
10.1016/j.cma.2018.12.037
发表时间：
2019-04
影响因子：
7.2
作者：
C. Chukwudozie;B. Bourdin;K. Yoshioka
通讯作者：
C. Chukwudozie;B. Bourdin;K. Yoshioka