Computational Methods for Heteroepitaxial Growth, Grain Boundary Motion, and High Frequency Wave Propagation

异质外延生长、晶界运动和高频波传播的计算方法

• 批准号: 0810113
• 负责人: Peter Smereka
• 金额: $ 25.64万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0810113&HistoricalAwards=false
• 关键词: Computational; Methods; Heteroepitaxial; Growth; Grain

This proposal involves three projects. The first concerns modeling andefficient simulation of heteroepitaxial growth using kinetic Monte Carlo and will build from prior NSF support which resulted in thedevelopment of a Fourier multigrid method for the fast solution ofdiscrete elastic equations for complex geometries. This work will be extended to develop methods for obtaining inexpensive upper bonds onrates, the use of local computations for elastic equations, and the inclusion ofintermixing of multiple species. The second project involves the simulation of grain boundary motion in two and three dimensions usinga recently developed multiphase variational level set framework whichallows one to systematically deduce level set equations for a network ofgrains moving under curvature flow. We plan to extend this formulation to allow the simulation of thousands of seeds by using only a few level setfunctions. The efficient computation of high frequency wave propagation and the semi-classical limit of the Schrodinger equation is the thirdproject. The proposed algorithm is based on the observation that most of the time, in these limiting regimes, the solutions are very localized in the wavenumber domain. This can be exploited by solving the equations in thisdomain using a fast local convolution. It is planned to update the solutionsby the computation of the matrix exponential using a Krylov subspaceapproach.Each of the proposed projects has the potential to have a significant impact on problems that are both fundamental and technologically important. Heteroepitaxial growth is scientifically interesting since it has effectson both nanoscales and mesoscales. It is technologically relevant sincequantum dot materials are made in this way. Our proposed techniques willgreatly increase the simulation speed thereby facilitating model development.The study of grain boundary motion using curvature flow is a classic problem in applied and computational mathematics which has importance in material science. Since there are no robust simulations of a large number grains in three dimensions the proposed project should have significant impact. The efficient computation of high frequency wave propagation has important facets ranging from antenna design to seismic sensing. On the other hand,fast simulation of the semi-classical limit of the Schrodinger equation could provide deeper insight into chemical reaction dynamics, molecular-surface scattering, and photodissociation, for example.

本提案涉及三个项目。第一个涉及使用动力学蒙特卡罗对异质外延生长进行建模和有效模拟，并将建立在先前 NSF 支持的基础上，从而开发了用于快速求解复杂几何形状的离散弹性方程的傅立叶多重网格方法。 这项工作将扩展到开发获得廉价的较高债券利率的方法、弹性方程局部计算的使用以及多种物种的混合。 第二个项目涉及使用最近开发的多相变分水平集框架模拟二维和三维晶界运动，该框架允许系统地推导在曲率流下移动的晶粒网络的水平集方程。我们计划扩展这个公式，以便仅使用几个水平集函数就可以模拟数千个种子。 第三个项目是高效计算高频波传播和薛定谔方程的半经典极限。所提出的算法基于这样的观察：大多数时候，在这些限制范围内，解非常局部化在波数域中。可以通过使用快速局部卷积求解该域中的方程来利用这一点。计划使用克雷洛夫子空间方法计算矩阵指数来更新解决方案。每个提议的项目都有可能对基础和技术上重要的问题产生重大影响。异质外延生长在科学上很有趣，因为它对纳米尺度和介观尺度都有影响。 这在技术上是相关的，因为量子点材料就是以这种方式制造的。 我们提出的技术将大大提高模拟速度，从而促进模型开发。利用曲率流研究晶界运动是应用和计算数学中的经典问题，在材料科学中具有重要意义。由于在三个维度上没有对大量颗粒进行可靠的模拟，因此拟议的项目应该会产生重大影响。高频波传播的有效计算具有从天线设计到地震传感的重要方面。 另一方面，薛定谔方程半经典极限的快速模拟可以提供对化学反应动力学、分子表面散射和光解离等更深入的了解。