伴随着不同尺度上的物理多样性和强耦合性，材料的性质会呈现出巨大的尺度效应，以及高度的各向异性与非均匀性。多尺度模型也就成为材料计算的自然选择。材料计算中的可计算建模与多尺度计算方法目前缺乏系统研究，这对我们既是机遇又是挑战。本项目通过整合物理和数学领域的活跃研究人员，针对材料辐照效应多尺度模拟中的耦合模型与算法；固体破坏模拟中的耦合模型与算法；大尺度复杂体系的电磁场计算等三个特定的复杂系统，利用多尺度模型和算法，对材料的复杂结构及其相变进行研究。本项目以具体问题为驱动，立足于特定系统的可计算物理模型与计算，在此基础上研究多尺度方法的基本数学理论和共性算法，所研究的内容具有重要的理论和实际意义。

Because of physical diversity and the strong coupling on different scales, material properties show huge size effect, high degree of anisotropy, and big inhomogeneity, suggesting multi-scale models are natural choices in computational materials science and calls for a systematical study on computable modeling and multi-scale algorithms. This provides us an opportunity as well as a challenge. The proposed project integrates active researchers from physics and mathematics in related fields to tackle three concrete examples of multiscale modeling, namely, multiscale models and algorithms in the simulation of radiation effects of materials; multiscale models and algorithms in the simulation of damages of solids; and multiscale models and algorithms in the simulation of electromagnetic field for large-scale complex systems. We will make use of multiscale models and algorithms to investigate the complexity of the material structure and its phase transition. Motivated by specific problems of practical interest, this project focuses on computable physical models and algorithms, while at the same time, study relevant fundamental mathematical theories and common algorithms. The proposed study is of great value both in theory and in practice.