相場模擬是計算材料科學的基礎工具之一，用於研究各種過程中的微觀結構演變，包括凝固、晶粒生長和固態相變。相場模型幾乎完全為數值求解，不同的應用需要不同數量的相場變量、不同形式的自由能函數，並且可能需要解附加的耦合方程（如，力學平衡），因此，不同應用之間的代碼移植非常困難。來自美國密西根大學材料科學與工程系的Stephen DeWitt團隊以及美國威斯康星州麥迪遜大學的合作者，開發了一個新的通用相場模擬框架PRISMS-PF（稜鏡-PF），使用了無矩陣變量的有限元方法，並結合了先進的自適應網格劃分和並行化策略。對兩種沉澱物所作的基準測試表明，在相同的誤差水平時，PRISMS-PF比一個基本的、定製的有限差分代碼快12倍。PRISMS-PF的第二個特點是其模塊化、以應用為中心的結構，使用戶能夠專注於感興趣的系統，而不是枯燥的代碼。PRISMS-PF核心庫還包括成核和多晶系統的功能，已通過其在一系列應用中的使用得到證明，包括沉澱成核、枝晶凝固、晶粒生長和腐蝕。這種新的框架提供了高性能、靈活性、易用性和開放性，從而推動材料科學領域的突破。該文近期發布於npj Computational Materials 6: 29 (2020)。
Editorial Summary
Discarding the single-purpose code: a general phase field simulation framework
The phase field model is one of the basic tools of Computational Materials Science, which is used to study the microstructure evolution in various processes, including solidification, grain growth and solid phase transformation. The phase field model is almost completely solved by numerical method. The phase field simulation on the length and time scale is computationally intensive. Therefore, when choosing numerical method, the calculation performance and parallel scalability are the primary consideration. In addition, simulation code written for one application can't be migrated to another without a lot of modifications.
Stephen DeWitt's team from the Department of materials science and engineering, University of Michigan and collaborators from the University of Madison, USA, developed a new open source community framework, PRISMS-PF, which is a key component of the open source multi-scale materials modeling framework developed by prism center. The computing and parallel scalability of PRISMS-PF can reach or exceed the typical phase field simulation code. The framework supports all kinds of phase field models, can create or modify the interface of a group of control equations simply and clearly, and can be separated from the numerical methods used to solve them as much as possible. In particular, the framework is open-source and can be widely adopted, modified and developed by members of the developer community. PRISMS-PF integrates with Materials Common information base and collaboration platform to collect, store and share detailed records of each simulation, providing high performance, ease of use, flexibility and adaptability to various applications. This article was recently published in npj Computational Materials 6, 29(2020).
原文Abstract及其翻譯
PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method (PRISMS-PF: 一種通用的無矩陣有限元相場模擬方法)
Stephen DeWitt, Shiva Rudraraju, David Montiel, W. Beck Andrews and Katsuyo Thornton
Abstract: 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.
摘要：本研究提出了一種強調性能、靈活性和易用性的新的相場模擬框架。實現這些目標所採用的策略包括使用無矩陣有限元方法和以應用程式為中心的模塊化代碼結構。這種方法是在新的開源PRISMS-PF框架中實現的。它的性能可以通過將無矩陣的有限元方法與自適應網格優化、顯式時間積分和多級並行處理相結合來實現。粒子生長問題的基準測試表明，採用自適應網格和高階單元的PRISMS-PF比採用二階精確空間離散和一階精確顯式時間積分的有限差分代碼快12倍。此外，對於二維固化基準問題，PRISMS-PF的性能達到或超過專注於隱式/半隱式時間步進的相場框架的性能，即使基準問題的計算量降低了顯式時間積分方案的可伸縮性優勢。PRISMS-PF支持任意數量的耦合控制方程。代碼結構通過將控制方程的定義與用於實現求解它們的數值方法分離，簡化了對這些控制方程的修改。作為模塊化設計的一部分，該框架包括成核和多晶體系的函數，可用於任何材料領域和拓寬研究對象。這種方法的多功能性通過幾種常見類型的相場模擬的例子得到了證明，包括調控組分後的粗化、凝固、沉澱、晶粒生長和腐蝕。
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