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.

该建议涉及三个项目。首先是使用动力学蒙特卡洛对异性生长进行建模和有效的模拟模拟，并将源于先前的NSF支持，从而导致了一种傅立叶多机方法，用于快速解决复杂几何形状的快速溶液弹性方程。 这项工作将扩展以开发用于获得廉价的上键Onrates的方法，用于弹性方程的局部计算以及包含多种物种的互化的方法。 第二个项目涉及使用最近开发的多相变分级框架在两个和三个维度中模拟晶粒边界运动，从而系统地推导了一个在曲率流下移动的网络的系统推导级别设置方程。我们计划扩展此公式，以允许仅使用几个级别的设置来模拟数千种种子。 高频波传播的有效计算和Schrodinger方程的半古典限制是第三个项目。所提出的算法是基于这样的观察结果，即在大多数情况下，在这些限制方案中，溶液在波数域中非常局部。可以通过使用快速的本地卷积求解此域中的方程来利用这一点。计划使用Krylov子paceaphacher进行矩阵指数的计算来更新解决方案。拟议项目的每个项目都有可能对既重要又具有技术重要的问题产生重大影响。杂质增长在科学上很有趣，因为它具有纳米级和介质的影响。 它在技术上是相关的，因为用这种方式制作了Quantum Dot材料。 我们提出的技术将详细提高模拟速度，从而促进模型开发。使用曲率流进行的晶界运动研究是在应用和计算数学中的经典问题，在材料科学中至关重要。由于在三个维度上没有大量晶粒的强大模拟，因此所提出的项目应产生重大影响。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，例如，快速模拟Schrodinger方程的半古典限制可以更深入地了解化学反应动力学，分子表面散射和光解异步。