A Splitting Scheme for the Numerical Solution of the KWC System
A Splitting Scheme for the Numerical Solution of the KWC System
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KWC系统数值解的分割方案
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
R. H. W. H. A. J. J. Winkle
中科院分区：
文献类型：
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作者：
R. H. W. H. A. J. J. Winkle
我们考虑了正则化小林-沃伦-卡特（KWC）系统数值解的分裂方法，该系统描述了不同方向的单晶颗粒在两个空间维度上的生长。 KWC 模型是一个由两个非线性抛物线偏微分方程组成的系统，表示与两个变量中的自由能相关的梯度流。基于后向欧拉方法的隐式时间离散，我们提出了一种分裂方法，并证明了解的存在性和能量稳定性。空间中的离散化由拉格朗日有限元处理，涉及计算域的几何一致、形状规则、单纯三角剖分，并且需要连续求解两个单独的离散椭圆问题。将时间视为参数，完全离散方程表示参数相关的非线性系统，该系统通过具有自适应选择时间步长的预测校正器连续策略来求解。数值结果说明了分裂方法的性能。 AMS学科分类：65M12、35K59、74N05
We consider a splitting method for the numerical solution of the regularized Kobayashi-Warren-Carter (KWC) system which describes the growth of single crystal particles of different orientations in two spatial dimensions. The KWC model is a system of two nonlinear parabolic PDEs representing gradient flows associated with a free energy in two variables. Based on an implicit time discretization by the backward Euler method, we suggest a splitting method and prove the existence as well as the energy stability of a solution. The discretization in space is taken care of by Lagrangian finite elements with respect to a geometrically conforming, shape regular, simplicial triangulation of the computational domain and requires the successive solution of two individual discrete elliptic problems. Viewing the time as a parameter, the fully discrete equations represent a parameter dependent nonlinear system which is solved by a predictor corrector continuation strategy with an adaptive choice of the time step size. Numerical results illustrate the performance of the splitting method. AMS subject classifications: 65M12,35K59,74N05