Postdoc: Adaptive Numerical Methods and Parallel Software Infrastructure for Materials Design

9503997我们这项建议的目的是开发自适应数值方法和相应的软件基础设施，用于求解材料科学中的LDA方程。目前基于快速傅立叶变换技术的求解方法不能准确地解析许多具有重要技术意义的材料中存在的短长度尺度。我们的自适应数值方法将把自适应网格加密技术与先进的多层数值特征值算法相结合。在高性能并行平台上实现自适应数值方法是困难的，因为程序员必须管理不规则分布的、动态变化的数据。自适应数值技术的使用将使理论材料科学家能够对无法用现有方法处理的复杂材料进行建模。此外，由于自适应方法可以应用于许多科学和工程学科，这项研究将影响其他领域，包括计算流体力学、半导体建模和地球物理建模。

9503997 Weare The purpose of this proposal is to develop adaptive numerical methods and the accompanying software infrastructure for the solution of the LDA equations in materials science. Current solution methods, based on Fast Fourier Transform techniques, cannot accurately resolve the short length scales present in many materials of technological importance. Our adaptive numerical methods will integrate adaptive mesh refinement techniques with advanced multilevel numerical eigenvalue algorithms. The implementation of adaptive numerical methods on high performance parallel platforms is difficult because the programmer must manage irregularly distributed, dynamically changing data. The use of adaptive numerical techniques will enable theoretical material scientists to model complex materials which cannot be treated using existing methods. Furthermore, because adaptive methods can be applied to a number of scientific and engineering disciplines, this research will impact other fields, including computational fluid dynamics, semiconductor modeling, and geophysical modeling.