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相场模拟是计算材料科学的基础工具之一，用于研究各种过程中的微观结构演变，包括凝固、晶粒生长和固态相变等等。相场模型几乎完全是数值求解的，在物理长度和时间尺度上进行的相场模拟是计算密集型的，因而，在选择数值方法时，首先需要考虑计算性能和并行可扩展性问题。此外，为某个应用编写的模拟代码一般不能用于另一个应用，需作大量修改方可。为了应对这些挑战，标准的方法是为每个应用开发不同的代码。然而这样做有很大的局限性：创建和维护多个独立的代码，每个代码都有自己的测试和文档。过去20年来，大量的工作集中在大大提高性能的技术上，如自适应网格增强和多级并行，但这些技术在用户开发的单用途代码中常常被忽略，因为它们的实现非常耗时。另一种模式是基于开发和利用开源社区，框架包含各种相场模型的构建块，为开发人员节省大量时间用于扩展框架的功能，而不是在新的单用途代码中实现基本功能。但这尚不知如何实现。
来自美国密歇根大学材料科学与工程系的Stephen DeWitt团队以及美国威斯康星州麦迪逊大学的合作者，开发了一个新的通用相场模拟框架PRISMS-PF，使用了无矩阵变量的有限元方法，并结合了先进的自适应网格划分和并行化策略。一项对两种沉淀物的基准测试表明，在相同的误差水平下，PRISMS-PF比一个基本的、定制的有限差分算法快12倍。PRISMS-PF的第二个特点是其模块化、以应用为中心的结构，使用户能够专注于感兴趣的系统，而不是枯燥的代码。PRISMS-PF核心库还包括成核和多晶系统的功能，已通过其在一系列应用中的使用得到证明，包括沉淀成核、枝晶凝固、晶粒生长和腐蚀。这种新的框架提供了高性能、灵活性、易用性和开放性，从而推动材料科学领域的突破。该文近期发表于npj Computational Materials 6: 29 (2020)，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。
PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method
Stephen De Witt, Shiva Rudraraju, David Montiel, W. Beck Andrews and Katsuyo Thornton
A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time- integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.
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