An adaptive, multilevel scheme for the implicit solution of three-dimensional phase-field equations
An adaptive, multilevel scheme for the implicit solution of three-dimensional phase-field equations
复制标题
三维相场方程隐式解的自适应多级方案
DOI：
10.1002/num.20634
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发表时间：
2010
影响因子：
3.9
通讯作者：
Green J
中科院分区：
文献类型：
--
作者：
Green J
相场模型由一组高度非线性耦合的抛物型偏微分方程组成，广泛用于模拟一系列凝固现象。本文着重于一个这样的模型，代表在三维空间的各向异性凝固的数值解。的工作的主要贡献是提出了一种解决方案的战略，结合层次网格自适应隐式时间积分和使用的非线性多重网格求解器在每一步。该策略在允许以自然方式并行计算的通用软件框架中实现。结果提供了定性和定量的理由，这些选择。© 2010年威利期刊公司。偏微分方程2010
Phase‐field models, consisting of a set of highly nonlinear coupled parabolic partial differential equations, are widely used for the simulation of a range of solidification phenomena. This article focuses on the numerical solution of one such model, representing anisotropic solidification in three space dimensions. The main contribution of the work is to propose a solution strategy that combines hierarchical mesh adaptivity with implicit time integration and the use of a nonlinear multigrid solver at each step. This strategy is implemented in a general software framework that permits parallel computation in a natural manner. Results are presented that provide both qualitative and quantitative justifications for these choices.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010