发表机构
University of Vienna（维也纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出分数阶阈值动力学算法模拟亚扩散晶粒生长，结合L1离散与Helmholtz扩散，实验表明较小分数阶加速粗化。
AI 中文摘要
我们提出了一种新的分数阶阈值动力学算法，用于亚扩散界面运动，并将其应用于多相晶粒生长模拟。该方法将Caputo时间导数的L1离散化与Helmholtz预解式阈值化步骤相结合。在每个时间层，L1卷积产生先前阈值化状态的凸历史平均值；然后通过Helmholtz扩散求解传播该依赖于历史的场，并通过阈值化将其投影回纯相。对于α=1，该方法简化为Merriman-Bence-Osher格式的Helmholtz预解式模拟，而对于0<α<1，它引入了亚扩散时间记忆。我们建立了变分刻画、最大值和比较原理，以及连续Helmholtz扩散步骤的稳定性。我们还在显式预解收缩假设下推导了记忆尾部估计和有限维钉扎准则。等张力多相方案在周期网格上实现。数值实验研究了L1历史和光滑长度的联合影响。固定步长运行表明，在测试范围内，较小的分数阶导致更快的粗化，而固定光滑长度的比较则考察了L1历史对连续更新的影响。
英文摘要
We propose a new fractional threshold-dynamics algorithm for subdiffusive interface motion and apply it to multiphase grain-growth simulations. The method combines the L1 discretization of the Caputo time derivative with a Helmholtz-resolvent thresholding step. At each time level, the L1 convolution produces a convex history average of the previously thresholded states; this history-dependent field is then propagated by a Helmholtz diffusion solve and projected back to pure phases by thresholding. For $α=1$, the method reduces to a Helmholtz-resolvent analogue of the Merriman-Bence-Osher scheme, whereas for $0<α<1$ it introduces a subdiffusive temporal memory. We establish a variational characterization, maximum and comparison principles, and stability for the continuous Helmholtz diffusion step. We also derive a memory-tail estimate and a finite-dimensional pinning criterion under an explicit resolvent-contraction hypothesis. The equal-tension multiphase scheme is implemented on periodic grids. The numerical experiments investigate the joint influence of the L1 history and the smoothing length. The fixed-step runs show faster coarsening for smaller fractional orders in the tested regime, while a comparison at fixed smoothing length examines the influence of the L1 history on successive updates.
