Conference on Adaptive Methods for Partial Differential Equations and Large-Scale Computation; October 11-12, 2003; Rensselaer Polytechnic Institute, Troy, New York

偏微分方程和大规模计算自适应方法会议；

• 批准号: 0318432
• 负责人: Peter Moore
• 金额: $ 0.5万
• 依托单位: Southern Methodist University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0318432&HistoricalAwards=false
• 关键词: Conference; Adaptive; Methods; Partial; Differential

Many physical phenomena in science and engineering are modeled by partial differential equations with solutions that exhibit localized non-uniformities. Such applications include boundary layers and shock waves in fluids and reaction fronts in combustion. Applications such as thin film coating, composite media and nano-scale materials require mathematical models capable of capturing behavior at several different scales. The traditional approach with user-designed meshes/methods is no longer acceptable in terms of cost and understanding of process behavior. The problems are too complex and users can be fooled. In some situations, the problems cannot be solved when using over-designed meshes. Adaptive methods and the accompanying data structures have become necessary for resolving different scales present in such applications. Over the last 20 years adaptive methods have matured to a point where they are used in many industrial applications. However, much is still to be done to obtain higher resolutions and more efficient adaptive methods. The investigator proposes to organize a conference with themes in (1) efficient adaptive refinement strategies; (2) data structures for parallel and adaptive computations; iii) a posteriori error estimation methods; (3) discontinuous Galerkin (DG) methods; (4) grid and mesh generation; and (5) multiscale techniques.The conference will bring together leading researchers working in this critical area of scientific computing to discuss new advances and challenges. It will also introduce young researchers to the area of adaptive methods for solving partial differential equations. The conference organizers have invited 14 plenary speakers to address those important issues in scientific computing and applications. It is expected that there will be around 60 participants in the conference. The conference organizer plans to publish the conference proceedings in the IMACS Journal on Applied Numerical Mathematics published by Elsevier-North-Holland. This is one of the leading numerical analysis journals that concentrates on the innovative solutions of partial differential equations.

科学和工程中的许多物理现象都是通过偏微分方程建模的，其解表现出局部不均匀性。此类应用包括流体中的边界层和冲击波以及燃烧中的反应前沿。薄膜涂层、复合介质和纳米级材料等应用需要能够捕获多种不同尺度行为的数学模型。就成本和对过程行为的理解而言，使用用户设计的网格/方法的传统方法不再可接受。问题太复杂，用户可能会被愚弄。在某些情况下，使用过度设计的网格无法解决问题。自适应方法和随附的数据结构已成为解决此类应用中存在的不同规模的必要条件。在过去的 20 年里，自适应方法已经成熟到可以在许多工业应用中使用的程度。然而，要获得更高分辨率和更有效的自适应方法还有很多工作要做。研究者建议组织一次会议，主题为（1）高效的自适应细化策略； (2) 用于并行和自适应计算的数据结构； iii) 后验误差估计方法； (3)间断伽辽金(DG)法； (4)网格及网格生成； (5) 多尺度技术。会议将汇集在科学计算这一关键领域工作的领先研究人员，讨论新的进展和挑战。它还将向年轻的研究人员介绍求解偏微分方程的自适应方法领域。会议组织者邀请了 14 位全体会议发言人来讨论科学计算和应用领域的重要问题。预计参会人数将在60人左右。会议组织者计划在 Elsevier-North-Holland 出版的 IMACS Journal on Applied Numerical Mathematics 上发表会议论文集。这是领先的数值分析期刊之一，专注于偏微分方程的创新解决方案。