Convergence of discrete and continuous unilateral flows for Ambrosio–Tortorelli energies and application to mechanics
Convergence of discrete and continuous unilateral flows for Ambrosio–Tortorelli energies and application to mechanics
复制标题
Ambrosio-Tortorelli 能量离散和连续单边流的收敛及其在力学中的应用
DOI：
10.1051/m2an/2018057
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
M. Negri
中科院分区：
文献类型：
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作者：
Stefano Almi;Sandro Belz;M. Negri
本文研究了Ginzburg-Landau相场断裂模型的交替最小化格式的收敛性。该算法的特点是缺乏不可逆性约束的相场变量的最小化，这种选择的优点，从计算的角度来看，是在效率的数值实现。不可逆性，然后恢复后验通过一个简单的逐点截断。我们利用时间离散化过程，采用一步或多（或无限）步交替最小化算法。我们证明了时间离散的解决方案收敛到一个单边L2梯度流的相场变量，满足平衡的力量和能量的身份。收敛证明在连续（Sobolev空间）设置和离散（有限元）设置，与任何停止标准的交替最小化计划。数值结果表明，多步格式具有更高的精度和更快的速度。它确实提供了很好的模拟大范围的时间增量，而一步计划只给出了非常小的时间增量可比的结果。
We study the convergence of an alternate minimization scheme for a Ginzburg–Landau phase-field model of fracture. This algorithm is characterized by the lack of irreversibility constraints in the minimization of the phase-field variable; the advantage of this choice, from a computational stand point, is in the efficiency of the numerical implementation. Irreversibility is then recovered a posteriori by a simple pointwise truncation. We exploit a time discretization procedure, with either a one-step or a multi (or infinite)-step alternate minimization algorithm. We prove that the time-discrete solutions converge to a unilateral L2-gradient flow with respect to the phase-field variable, satisfying equilibrium of forces and energy identity. Convergence is proved in the continuous (Sobolev space) setting and in a discrete (finite element) setting, with any stopping criterion for the alternate minimization scheme. Numerical results show that the multi-step scheme is both more accurate and faster. It provides indeed good simulations for a large range of time increments, while the one-step scheme gives comparable results only for very small time increments.
《极端条件下的XMCD研究——巡回电子系统中的磁相变——》（特邀）
DOI：
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发表时间：
2007
期刊：
影响因子：
--
作者：
H.;Maruyama
通讯作者：
Maruyama