International Workshop on Numerical Analysis of Singularly Perturbed Differential Equations

奇摄动微分方程数值分析国际研讨会

• 批准号: 1632111
• 负责人: James Adler
• 金额: $ 1万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-06-15 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1632111&HistoricalAwards=false
• 关键词: International; Workshop; Numerical; Analysis; Singularly

Computational Mathematics, in general, and Numerical Analysis and Scientific Computing (NASC), in particular, are now well-recognized as providing a "third mode" of scientific investigation, complementing traditional theoretical and experimental approaches. While the successes of NASC in both basic science and industry are many, one class of problems that remains challenging are those with rapid changes in the simulated quantities, such as arise with boundary and interior layers in fluid dynamics and other disciplines. This grant supports US participation in an international workshop and short course on "Numerical Analysis for Singularly Perturbed Differential Equations", to be held on the campus of St. Mary's University in Halifax (Canada), from July 25-29, 2016. NSF funds will allow US-based participants to benefit from learning both the basic tools in this area and the state-of-the-art, developing new collaborations with researchers from Canada and abroad. The PI will prioritize support for participants from underrepresented groups.Problems with boundary and interior layers arise in many areas of scientific and industrial simulation, including mathematical biology, fluid dynamics, and electromagnetics. Efficient parameter-robust simulation tools are needed in these fields to support the ever-increasing complexity of applied problems of interest to scientists and engineers. Broadly, these problems can be categorized as ``singular perturbation problems", where a small parameter is identified that controls the width of these critical layers. In the limit as these parameters approach zero, nearly all standard discretization and mesh-refinement strategies fail to yield robust error control; thus, a specialized subfield of NASC has arisen to address efficient and robust simulation of singularly perturbed differential equations. This two-day short course will focus on finite-difference and finite-element discretizations on fitted-layer meshes, as well as adaptive mesh refinement strategies for these problems. The remainder of the workshop is aimed at collaborative research sessions among workshop participants to apply these tools to real-world problems. There are many opportunities for broader impacts of the proposed short course and workshop, including the development of new interdisciplinary research connections.

计算数学，特别是数值分析和科学计算（NASC），现在被公认为提供了科学研究的“第三种模式”，补充了传统的理论和实验方法。 尽管NASC在基础科学和工业领域取得了许多成功，但仍然具有挑战性的一类问题是模拟量快速变化的问题，例如流体动力学和其他学科中的边界层和内部层所出现的问题。 这笔赠款支持美国参加将于 2016 年 7 月 25 日至 29 日在哈利法克斯（加拿大）圣玛丽大学校园举办的“奇扰微分方程数值分析”国际研讨会和短期课程。 NSF 基金将使美国的参与者受益于学习该领域的基本工具和最先进的技术，并与加拿大和国外的研究人员开展新的合作。 PI 将优先支持来自代表性不足群体的参与者。边界层和内部层的问题出现在科学和工业模拟的许多领域，包括数学生物学、流体动力学和电磁学。 这些领域需要高效的参数鲁棒性仿真工具来支持科学家和工程师感兴趣的应用问题日益复杂的情况。 从广义上讲，这些问题可以归类为“奇异扰动问题”，其中确定了一个小参数来控制这些关键层的宽度。在这些参数接近零的极限下，几乎所有标准离散化和网格细化策略都无法解决产生鲁棒误差控制；因此，NASC 的一个专门子领域出现了，用于解决奇扰动微分方程的高效和鲁棒模拟问题，这个为期两天的短期课程将重点关注有限差分和有限元离散化。拟合层网格，以及针对这些问题的自适应网格细化策略，研讨会的其余部分旨在研讨会参与者之间的协作研究会议，以将这些工具应用于现实世界的问题。短期课程和研讨会，包括发展新的跨学科研究联系。