Ninth Copper Mountain Conference On Multigrid Methods

第九届铜山多重网格方法会议

• 批准号: 9816592
• 负责人: Steve McCormick
• 金额: $ 4万
• 依托单位: Front Range Scientific Computations, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-10-01 至 2002-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9816592&HistoricalAwards=false
• 关键词: Ninth; Copper; Mountain; Conference; Multigrid

McCormick9816592The investigator and his colleagues organize a series of annual Copper Mountain Conferences. The subject of these meetings alternates between multigrid methods in odd-numbered years and iterative methods in even-numbered years. The Copper Mountain Conferences provide a forum for the exchange of ideas in these two closely related fields. The program for a conference in this series consists of tutorials, invited lectures, and contributed papers, as well as time for scientific interaction among the participants. Topics of emphasis for the conferences include advanced architectures, algebraic-type methods, and nonsymmetric linear systems. This grant provides support for students to participate in the conferences.The mathematical description of real-world problems leads inevitably to equations to solve. Many times the equations are nonlinear ones, arising because the underlying problem is nonlinear. Often, however, the original problem is linear and the mathematical equations are too. Such problems arise in all areas of science and technology, and are of special interest in biology, materials, environmental studies, and manufacturing. Progress in these areas requires solution of more comprehensive modeling equations --- such models are usually more nonlinear than simpler models ---, or more accurate solution of existing models --- increasing the size of the numerical problem to be solved. Many problems lead to equations that are not symmetric; computational methods for such problems offer special difficulties. Numerical methods for solving a differential equation usually begin by imposing a grid on the region where the equation holds. From the differential equation, algebraic equations are then developed; their solution represents the solution of the differential equation. The accuracy of the approximate solution commonly is measured by the fineness of the grid. Multigrid methods are numerical methods for solving partial differential equations that systematically exploit the relationship between approximate solutions on different grids to arrive at a solution whose accuracy is consistent with the finest grid but for considerably less work. The methods are often dramatically more efficient than others. The conferences address advances in iterative methods and in multigrid methods to deal with larger numerical systems, nonsymmetric and nonlinear systems, and the use of multiprocessor computers. The methods are of great practical import in engineering, manufacturing, materials, physics, and fluid dynamics. This project supports student participants at the Copper Mountain conferences on multigrid methods and on iterative methods. The students present a talk on their research in the regular sessions of the conference. The primary objective here is to encourage student participation in these rapidly evolving areas, and to provide an excellent opportunity for these students to demonstrate their new results, to learn more about the field from its experts, and to become a more integral part of the discipline. Supporting student participation is critical for developing the next generation of scientists and engineers.

这位研究者和他的同事们组织了一系列的年度铜山会议。这些会议的主题在奇数年的多重网格方法和偶数年的迭代方法之间交替进行。铜山会议为这两个密切相关领域的思想交流提供了一个论坛。该系列会议的计划包括教程、特邀演讲和投稿论文，以及参与者之间的科学互动时间。会议的重点主题包括高级体系结构、代数型方法和非对称线性系统。这项资助为学生参加会议提供支持。对现实世界问题的数学描述不可避免地导致需要求解的方程。很多时候这些方程是非线性的，因为潜在的问题是非线性的。然而，通常最初的问题是线性的，数学方程也是线性的。这些问题出现在所有的科学和技术领域，在生物学、材料、环境研究和制造业中特别有趣。这些领域的进展需要解决更全面的建模方程——这样的模型通常比简单的模型更非线性——或者更精确地解决现有模型——增加待解决的数值问题的规模。许多问题导致方程不是对称的；这类问题的计算方法有特殊的困难。求解微分方程的数值方法通常首先在方程所在的区域上加一个网格。由微分方程推导出代数方程；它们的解表示微分方程的解。近似解的精度通常是用网格的精细度来衡量的。多重网格法是一种求解偏微分方程的数值方法，它系统地利用不同网格上的近似解之间的关系，从而得到精度与最优网格一致但工作量相当少的解。这些方法通常比其他方法要有效得多。会议讨论了迭代方法和多网格方法的进展，以处理较大的数值系统，非对称和非线性系统，以及多处理器计算机的使用。这些方法在工程、制造、材料、物理和流体动力学方面具有重要的实际意义。该项目支持参加铜山会议的学生学习多网格方法和迭代方法。学生们在会议的定期会议上就他们的研究作报告。这里的主要目标是鼓励学生参与这些快速发展的领域，并为这些学生提供一个绝佳的机会来展示他们的新成果，从专家那里更多地了解该领域，并成为该学科更不可或缺的一部分。支持学生的参与对于培养下一代科学家和工程师至关重要。