论文标题
用于求解脆性断裂的单片相位模型的非线性野外预处理
Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture
论文作者
论文摘要
预测裂纹传播，成核和相互作用的最先进策略之一是相位场方法。尽管具有可靠性和鲁棒性，但相位场的方法仍遭受着繁重的计算成本，这是由于基础能量功能的非跨性别性以及解决损害梯度所需的大量未知数所致。在这项工作中，我们建议使用Schwarz预处理牛顿（SPIN）方法以单片方式解决此类非线性系统。提出的自旋方法利用了场拆分方法，并以累加和乘法方式将能量功能分别相对于位移和相位场分别最小化。与标准交替的最小化相反，这种解耦最小化过程的结果用于在每个牛顿的迭代中构建一个耦合线性系统的预处理。通过几个数值示例研究了所提出的添加剂和乘法旋转方法的总体性能和收敛性。还进行了与广泛使用的替代最小化的比较，我们显示执行时间的减少至50倍。此外，我们还证明，随着问题大小的增加和更大的负载增量，这种减少的增长甚至进一步增长。
One of the state-of-the-art strategies for predicting crack propagation, nucleation, and interaction is the phase-field approach. Despite its reliability and robustness, the phase-field approach suffers from burdensome computational cost, caused by the non-convexity of the underlying energy functional and a large number of unknowns required to resolve the damage gradients. In this work, we propose to solve such nonlinear systems in a monolithic manner using the Schwarz preconditioned inexact Newton's (SPIN) method. The proposed SPIN method leverages the field split approach and minimizes the energy functional separately with respect to displacement and the phase-field, in an additive and multiplicative manner. In contrast to the standard alternate minimization, the result of this decoupled minimization process is used to construct a preconditioner for a coupled linear system, arising at each Newton's iteration. The overall performance and the convergence properties of the proposed additive and multiplicative SPIN methods are investigated by means of several numerical examples. Comparison with widely-used alternate minimization is also performed and we show a reduction in the execution time up to a factor of 50. Moreover, we also demonstrate that this reduction grows even further with increasing problem size and larger loading increments.
