Workshop on Preservation of Stability Under Discretization

离散化下保持稳定性研讨会

• 批准号: 0102878
• 负责人: Donald Estep
• 金额: $ 1.26万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-05-15 至 2002-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0102878&HistoricalAwards=false
• 关键词: Workshop; Preservation; Stability; Under; Discretization

Stability is a term used to describe a wide variety of issues revolving around the physical observability of a solution of a differential equation. Stability lies at the very heart of the ability to make predictions about physical situations from mathematics and are particularly relevant when numerical approximation is involved, since discretization causes perturbation of both the model and the data. Numerical stability issues are typically complex because addressing such questions often requires a wide range of mathematical techniques, involving not only standard methods of numerical analysis, but ideas from dynamical systems, geometry, functional analysis, and the theory of differential equations. This raises barriers both to young researchers trying to learn about numerical stability and to communication between researchers working in different areas yet facing similar stability problems. The goal of the Workshop on the Preservation of Stability under Discretization is twofold: (1) to increase the accessibility of numerical stability issues for young researchers and (2) provide an opportunity for the exchange of information and ideas between specialists in different application areas. The Workshop will host a series of lectures by leading experts, each of whom will each address a separate aspect of stability under discretization. The lectures will be aimed towards an audience of advanced graduate students and non-specialists and will be collected into a permanent archive. In addition, the invited speakers will host a series of discussion and analysis sessions for students and young researchers.Stability is the term used to describe the situation in which a physical quantity is affected by small disturbances taking place at remote distances and times. The "butterfly" effect in chaos is one well-known stability issue, but stability issues arise in nearly every kind of physical situation from the flow of fluids and gases to computing rocket trajectories to other planets. Stability is particular relevant to numerical modeling of physical situations on computers because the modeling itself induces widespread error/disturbances. Accounting for the effects of these discretization errors is difficult because it typically requires mathematical ideas from many areas, raising barriers both to learning about how deal with stability and to communication between different areas of specialization. The goal of the Workshop on the Preservation of Stability under Discretization is twofold: (1) to increase the accessibility of numerical stability issues for young researchers and (2) provide an opportunity for the exchange of information and ideas between specialists in different application areas. The Workshop will host a series of lectures by leading experts, each of whom will each address a separate aspect of stability under discretization. The lectures will be aimed towards an audience of advanced graduate students and non-specialists and will be collected into a permanent archive. In addition, the invited speakers will host a series of discussion and analysis sessions for students and young researchers.

稳定性是一个术语，用来描述围绕微分方程解的物理可观察性的各种各样的问题。稳定性是通过数学对物理情况进行预测的能力的核心，当涉及数值近似时，稳定性尤为重要，因为离散化会导致模型和数据的扰动。数值稳定性问题通常是复杂的，因为解决这类问题往往需要广泛的数学技术，不仅涉及数值分析的标准方法，还涉及动力系统、几何、泛函分析和微分方程理论的思想。这给试图学习数值稳定性的年轻研究人员和在不同领域工作但面临类似稳定性问题的研究人员之间的交流增加了障碍。离散化下保持稳定性研讨会的目标有两个：(1)增加年轻研究人员对数值稳定性问题的可及性；(2)为不同应用领域的专家提供交流信息和思想的机会。讲习班将由主要专家主持一系列讲座，每位专家将分别讨论离散化下稳定性的一个方面。讲座将以高级研究生和非专业人士为对象，并将被收集成永久档案。此外，受邀演讲者将为学生和青年研究人员主持一系列讨论和分析会议。稳定性是用来描述一个物理量受到发生在遥远距离和时间的小扰动影响的情况的术语。混沌中的“蝴蝶”效应是一个众所周知的稳定性问题，但稳定性问题几乎出现在每一种物理情况中，从流体和气体的流动到计算飞往其他行星的火箭轨迹。稳定性与计算机上物理情况的数值模拟特别相关，因为模拟本身会引起广泛的误差/干扰。考虑这些离散化误差的影响是困难的，因为它通常需要来自许多领域的数学思想，这增加了学习如何处理稳定性和不同专业领域之间沟通的障碍。离散化下保持稳定性研讨会的目标有两个：(1)增加年轻研究人员对数值稳定性问题的可及性；(2)为不同应用领域的专家提供交流信息和思想的机会。讲习班将由主要专家主持一系列讲座，每位专家将分别讨论离散化下稳定性的一个方面。讲座将以高级研究生和非专业人士为对象，并将被收集成永久档案。此外，受邀演讲者将为学生和青年研究人员主持一系列讨论和分析会议。