IMACS Workshop on Adaptive Methods for Partial Differential Equations

偏微分方程（PDE）的自适应方法是最有效的计算方法，在许多重要的科学和工程应用中出现的一大类偏微分方程。这一领域在过去二十年中稳步增长。该研讨会将汇集来自世界各地的顶尖研究人员，讨论偏微分方程自适应方法的理论和计算方面，并促进数学家、工程师和科学家之间更强有力的合作。主题包括后验误差估计，自适应h-p精化，复杂几何的自适应性，自适应编码的实现，移动网格技术和应用，自适应谱方法，非线性分析，自适应建模和自适应方法的应用。 该项目将补充加拿大的资金，以支助将于2002年8月在多伦多菲尔兹数学研究所举行的IMACS偏微分方程自适应方法讲习班。IMACS是国际数学和计算机仿真协会。 这个研讨会是为期一年的计划的一部分，重点是数值计算-有史以来第一次在菲尔兹研究所。该计划认识到数值分析在推进计算科学和工程中的核心重要性，并寻求扩大数学家，科学家和工程师之间的互动。这笔资金将用于支持来自美国的研究人员的差旅费，包括特邀演讲人和研究生或博士后级别的年轻研究人员。 研讨会上讨论的主题将是广泛的，但将包括最佳自适应策略，高性能计算，误差估计，实施问题，几何考虑和应用。应用将涉及流体流动，优化设计和制造，电磁现象，生物力学和生物材料。

Adaptive methods for partial differential equations (PDEs) are the most effective computational approach for a large class of PDEs that arise in many important applications in science and engineering. This area has grown steadily during the past two decades. This workshop will bring together leading researchers from around the world to address both theoretical and computational aspects of adaptive methods for PDEs and to foster stronger collaboration between mathematicians, engineers and scientists. Topics include a posteriori error estimation, adaptive h-p refinement, adaptivity with complex geometry, implementation of adaptive codes, moving mesh techniques and applications, adaptive spectral methods, nonlinear analysis, adaptive modeling and applications of adaptive methods. This project will supplement Canadian funding to support the IMACS Workshop on Adaptive Methods for Partial Differential Equations to be held at the Fields Institute of Mathematics in Toronto in August 2002. IMACS is the International Association for Mathematics and Computers in Simulation. This workshop is part of a year-long program focusing on numerical computation - the first ever at the Fields Institute. The program recognizes the central importance of numerical analysis in advancing computational science and engineering, and seeks to expand interactions among mathematicians, scientists, and engineers. The funds will be used to support travel expenses of researchers from the U.S., including invited speakers and young researchers at the graduate or postdoctoral level. Topics discussed at the workshop will be far ranging but will include optimal adaptive strategies, high-performance computation, error estimation, implementation issues, geometrical considerations, and applications. Applications will involve fluid flow, optimal design and manufacturing, electromagnetic phenomena, and biomechanics and biomaterials.