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用偏微分方程解表现出局部化的非一致性来建模的。这类应用包括流体中的边界层和激波以及燃烧中的反应前沿。薄膜涂层、复合介质和纳米材料等应用需要能够在几个不同尺度上捕捉行为的数学模型。在成本和对进程行为的理解方面，使用用户设计的网格/方法的传统方法不再可接受。这些问题太复杂了，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这些问题。为了解决这种应用中存在的不同尺度，自适应方法和伴随的数据结构已经变得必要。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，要获得更高的分辨率和更有效的自适应方法，仍有很多工作要做。研究人员建议组织一次会议，主题包括(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；(Iii)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。会议将聚集在这一关键科学计算领域的领先研究人员，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名全体演讲者来讨论科学计算和应用中的这些重要问题。预计将有60人左右参加会议。会议组织者计划将会议记录发表在爱思唯尔-北荷兰公司出版的iMACS应用数值数学杂志上。这是主要的数值分析杂志之一，专注于偏微分方程解的创新。

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.