Multiscale Computations of Time Dependent Highly Oscillatory Systems

瞬态高振荡系统的多尺度计算

• 批准号: 1522792
• 负责人: Bjorn Engquist
• 金额: $ 19.09万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1522792&HistoricalAwards=false
• 关键词: Multiscale; Computations; Time; Dependent; Highly

Many important systems in science, engineering, and industry are modeled by dynamical systems with solutions that are highly oscillatory relative to the overall time scale. Molecular dynamics computations for materials science and biology are of this form and so is simulation of neural processes. Such systems pose severe challenges to numerical simulations. In direct simulations each oscillation must be resolved over the full time interval, which is highly computationally costly. This research project aims to develop new computational methods that are well suited to simulation of such systems. An example of the infinite-dimensional systems that will be considered is high frequency wave propagation. One goal is improving the quality of seismic imaging. Earlier contributions have successfully handled cases with strong separation of large and small scales in the solutions by only applying microscale simulations locally. The current work aims at reducing this requirement by adaptively monitoring the solution and exploiting parallel-in-time computations. This research will go one step further than the typical analytical or numerical averaging and homogenization approaches to deal with more challenging multiscale problems where there is no clear scale separation. The research will start to establish a new multiscale framework, which will support adaptive application of microscale models in small parts of the computational domain. The computational efficiency will result partially from parallelization in time. The theoretical goal is to establish a mathematical link between averaging theories to existing parallel-in-time computational frameworks and filtering techniques. The practical goal is to prepare the study of seismic wave propagation where the microscale model describes detailed diffraction and the effective macroscales are represented by geometrical optics type models.

科学、工程和工业中的许多重要系统都是由动力系统建模的，其解相对于整个时间尺度是高度振荡的。 材料科学和生物学的分子动力学计算就是这种形式，神经过程的模拟也是如此。这样的系统对数值模拟提出了严峻的挑战。在直接模拟中，必须在整个时间间隔内解决每个振荡，这是非常昂贵的计算。该研究项目旨在开发新的计算方法，非常适合模拟此类系统。将考虑的无限维系统的一个例子是高频波传播。一个目标是提高地震成像的质量。早期的贡献已经成功地处理的情况下，强大的分离的大规模和小规模的解决方案，只适用于微尺度模拟本地。目前的工作旨在通过自适应监控解决方案和利用并行时间计算来降低这一要求。这项研究将比典型的分析或数值平均和均匀化方法更进一步，以处理没有明确尺度分离的更具挑战性的多尺度问题。该研究将开始建立一个新的多尺度框架，这将支持微尺度模型在计算域的小部分中的自适应应用。计算效率将部分来自时间上的并行化。理论上的目标是建立一个数学平均理论之间的联系，现有的并行计算框架和过滤技术。实际目标是准备研究地震波传播，其中微观模型描述详细的衍射，有效的宏观尺度由几何光学类型的模型表示。