本项目是高水平的交流与研讨项目，拟邀请国际著名数学家和国内处于前沿水平的院士、专家学者，对计算数学领域的相场模型热点问题展开深度交流与合作，讨论数学建模和高精度算法及应用实现的关键问题。主要研究主题涉及经典传统相场模型和多相复杂相场模型的数值模拟研究，探讨高效稳定的数值方法，考虑数值格式的物理特性和实际应用的高效性；同时，进一步关注非局部相场模型的数学建模、数学理论和数值方法的研究。并与实际问题相结合，解决材料科学、金融科学以及图像处理等方面的科学问题。此次交流研讨活动，可以提高参加活动人员对相关问题背景更深入的了解、吸引更多的科研人员加入到相关问题的研究，促进关键科学问题的解决，合作撰写发表高质量科研论文。

This program is supported by the Tianyuan Mathematics Exchange Program of NSFC. It aims to provide a forum for researchers in China and overseas to exchange ideas on high-order and related numerical methods and applications of local and nonlocal phase-field equations. It also aims to promote collaborative research in these fields..In this program, the international and domestic famous mathematicians will be invited. We will explore the hot issues of the phase-field models in the field of computational mathematics and have cooperation on them. Meanwhile, we will discuss the mathematical modeling and the high-order numerical methods. The main research topic involves the numerical simulation research of the classical phase-field models and multiphase complex phase-field models, discussion of the efficient and stable numerical method, the physical characteristics of numerical schemes and the efficiency of practical application. At the same time, we will pay further attention to the nonlocal phase field models, which include the mathematical modeling, mathematical theory and numerical methods. And combined with practical problems, we will solve scientific problems in material science, financial science and image processing.