Numerical Simulation of Materials Microstructural Evolutions

这个项目使PI，一个应用数学家和数值分析师，在宾夕法尼亚州立大学材料科学与工程（MSE）部门花了一年的时间，沉浸在MSE部门的全面研究和教育活动中，并与他的主持人进行材料微观结构演变的数值模拟的联合研究。微观结构演变将通过使用连续场方法来建模，该方法可以得到一组可以严格分析的良好定姿的偏微分方程。求解这些方程的有效和准确的数值方案/软件将被开发、验证并应用于当前感兴趣的许多具有挑战性的问题。该项目不仅将扩大对重要的数学进步和最先进的数值方法/软件的认识和使用，这些方法和软件有可能对材料科学产生重大影响，产生改进的模型和数值方案，这将有助于更好地理解微观结构演变的复杂过程，并提供新的基本的、实用的见解，为美国工业提供竞争优势。也为数学系和MSE系之间更广泛的持久合作奠定了基础。该IGMS项目由MPS多学科活动办公室（OMA）和数学科学司（DMS）联合支持。

This project enables the PI, an applied mathematician and numerical analyst, to spend a year in the Materials Science and Engineering (MSE) department at Penn State, immerse himself in the full research and educational activities of the MSE department, and conduct a joint research with his hosts on numerical simulation of materials microstructural evolution.The microstructural evolution will be modeled by using a continuum field approach which results in a set of well-posed partial differential equations that can be rigorously analyzed. Efficient and accurate numerical schemes/software for solving these equations will be developed, validated and applied to a number of challenging problems of current interest.This project will not only expand the awareness and use of important mathematical advances and state-of-the-art numerical methods/software which have the potential to make significant impact on the materials science, result in improved models and numerical schemes which will contribute to a better understanding of the complex process of microstructural evolution, and provide new fundamental, practical insights which can provide US industry with a competitive edge, but also set up the stage for a lastingcollaboration in a broader scale between the Math and MSE departments.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).