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

科学和工程中的许多物理现象都是由偏微分方程模拟的，其解具有局部非均匀性。这些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在几个不同尺度下捕获行为的数学模型。在成本和对过程行为的理解方面，用户设计的网格/方法的传统方法不再是可接受的。问题太复杂，用户可能会被愚弄。在某些情况下，当使用过度设计的网格时，这些问题无法解决。自适应的方法和相应的数据结构已经成为解决这些应用中存在的不同尺度的必要条件。在过去的20年中，自适应方法已经成熟到在许多工业应用中使用的程度。然而，仍有许多工作要做，以获得更高的分辨率和更有效的自适应方法。研究者建议组织一次会议，主题是：（1）有效的自适应精化策略;（2）并行和自适应计算的数据结构;（3）后验误差估计方法;（3）不连续Galerkin（DG）方法;（4）网格和网格生成;以及（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，挑战它还将向年轻研究人员介绍解决偏微分方程的自适应方法。会议组织者邀请了14名全体发言人，讨论科学计算和应用中的这些重要问题。预计将有约60人参加会议。会议组织者计划在由Elsevier-North-Holland出版的IMACS Journal on Applied Numerical Mathematics上发表会议记录。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。

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.