U.S.-Switzerland Cooperative Research on Order Stars, Riemann Surfaces, and Implicit Solutions of Hyperbolic Problems (Applied Mathematics)

该奖项支持亚利桑那州的迷迭香·勒诺教授 州立大学合作开展数学研究 应用数学教授罗尔夫·杰尔奇 瑞士联邦研究所小组，苏黎世。 他们正在研究某些数值的稳定性 双曲型微分的算法 方程 通常，这些问题的数值解 微分方程可以通过各种方法得到， 方法，如有限元，谱方法和 有限差分法 在这个提议中， 强调差异化方法。 双曲型初边值问题的实解 在许多领域都需要解决问题，包括 计算流体力学、物理学和 空气动力学 一个完整的几何描述的 黎曼曲面的星星级将提供对 数值算法的稳定性和精度， 解决这些问题。 两位研究人员都积极参与 在双曲方程的数值解;博士。 Renaut的工作主要集中在波浪上 方程，而杰尔奇博士一直致力于平流 方程 许多其他问题将受益于一个 更深入地理解这些数值算法。

This award supports Professor Rosemary Renaut of Arizona State University to collaborate in mathematics research with Professor Rolf Jeltsch of the Applied Mathematics Group of the Swiss Federal Institute (ETH), Zurich. They are studying the stability of certain numerical algorithms for solving hyperbolic differential equations. Typically, numerical solutions to these differential equations can be found by a variety of methods such as finite elements, spectral methods and finite difference methods. In this proposal finite difference methods are emphasized. Realistic solutions of hyperbolic initial boundary value problems are required in many areas including computational fluid mechanics, geophysics and aerodynamics. A complete geometric description of the order star of Riemann surfaces will provide insight into the stability and accuracy of numerical algorithms to solve these problems. Both researchers have been active in the numerical solution of hyperbolic equations; Dr. Renaut's work has been mainly concentrated on the wave equation, while Dr. Jeltsch has worked on the advection equation. Many other problems will benefit from a deeper understanding of these numerical algorithms.