Ninth Copper Mountain Conference On Multigrid Methods

麦考密克9816592调查员和他的同事们组织了一系列年度铜山会议。这些会议的主题在奇数年的多重网格法和偶数年的迭代方法之间交替。铜山会议为在这两个密切相关的领域交流思想提供了一个论坛。这一系列会议的计划包括教程、特邀讲座和投稿论文，以及与会者之间的科学互动时间。会议的重点主题包括先进的体系结构、代数型方法和非对称线性系统。这笔助学金为学生参与会议提供了支持。对现实世界问题的数学描述不可避免地会导致方程的求解。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，最初的问题往往是线性的，数学方程也是线性的。这样的问题出现在科学和技术的所有领域，在生物学、材料、环境研究和制造业中尤其令人感兴趣。这些领域的进展需要求解更全面的建模方程-这类模型通常比更简单的模型更具非线性-或者现有模型的更准确的解-增加要解决的数值问题的规模。许多问题导致方程不对称；这类问题的计算方法特别困难。求解微分方程的数值方法通常首先在方程所在的区域上施加网格。从微分方程式出发，发展出代数方程；它们的解代表了微分方程式的解。近似解的精度通常用网格的细度来衡量。多重网格法是一种求解偏微分方程组的数值方法，它系统地利用不同网格上近似解之间的关系，得到一个精度与最细网格一致但工作量相当小的解。这些方法往往比其他方法效率高得多。这些会议讨论了迭代方法和多重网格方法的进展，以处理更大的数值系统、非对称和非线性系统，以及多处理器计算机的使用。该方法在工程、制造、材料、物理、流体力学等领域具有重要的实用价值。该项目支持参加铜山会议的学生参加关于多重网格方法和迭代方法的会议。学生们在会议的定期会议上发表了关于他们的研究的报告。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极好的机会来展示他们的新成果，从专家那里了解更多关于该领域的知识，并成为该学科更不可或缺的一部分。支持学生参与对于培养下一代科学家和工程师至关重要。

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.